Step 1 The search:
An obvious place to start your search would be google. You might type in something like "property in Fethiye," or "real estate Fethiye" - you'd get lots of hits and think you were on a roll. The problem with this is that you are only going to get results from agents. As with most every country in the world, it is cheaper to buy from an actual person - check out Sahibinden - this link will take you through to the English version of the site. "sahibinden" means from the owner - some of the house are, some aren't. The real estate agents have the bonus factor that a lot of them can speak some vague semblance of English. If you go directly to the owner you will almost certainly need someone Turkish to speak for you. This may sound daunting, but here's the thing if you are wanting to move to Turkey you need to get used to things being in Turkish. Everything is. You can pay for translators, you can make some friends at a bar and get them to help you out, you can trust to luck that there will be an English speaker around whenever you need to do something: but essentially you need a plan for dealing with life in a foreign country. This is just the first step. The bonus of doing it now is that houses from owners are often 10 to 20,000 lira cheaper than those offered by real estate agents - seriously it is worth making the effort.
Note, I haven't found estate agents distrustworthy, but I have found them to often be very poor at their jobs, you can read about that here. If you do feel safer with a real estate agent check out the views and reviews on this forum, and if you are adverse to any type of risk at all the guy who set up this forum also has an estate agency - he is by all accounts totally trustworthy and generally awesome. Husband and I did not feel the need to be ultra safe, as we trusted ourselves to spot the charlatans (more on that later.)
Alongside sahibinden, milliyet emlak is a good one to check out, though the English version often seems to have kinks in (note. if you use the google-english-translate function it converts the prices by simply swapping the TL for a pound sign - this is not accurate.) For properties being sold by English people check out the local classifieds, and the fethiye buy-sell-rent group on facebook.
A note about property in Turkey - there are a lot of new houses. New is by no means a guarantee of quality, but they sure look pretty! Every year more new houses are built, they are even prettier! This means that if you bought a new house, then want to sell it only a few years later, unless you have done magical things with it, or are in a really really good location, it will almost certainly have dropped in value. English people (apologies for the sweeping generalisation) by and large, don't get this - it took me a while to get it. Your home will eventually go up in value (provided you didn't pay silly money for it to start with) but if you are looking for a quick turnaround study the market and remember people like pretty things. Ten years is a lot more viable time frame to make money on your property. Anyway the point of this - if you buy from English people they are often pricing their properties a lot higher than a Turkish person would in the same situation,partly for this reason and partly because English people seem to end up paying more to start with. Houses are cheaper in Turkey, a lot lot cheaper than the UK, don't just settle for "wow this seems cheap!" it is but check it is a good price for Turkey, not the UK.
During the summer season house prices go up because a lot of tourists (both Turkish and foreign) are buying, the cheapest time of year is winter.
Step 2 The viewing
Surveyors are not a thing in Turkey. When a bank grants you a mortgage, they may or may not come to see the property. Sometimes they swing by and count the bedrooms, but mostly they just check the set value of you property on their computer and say how much they will lend based on that. This means you need to be the surveyor. Check the windows (often badly fitted,) check for dampness and humidity (endemic in Fethiye) - look for new paint, mould, weird smells, bring a humidity tester with you. Check to roof space - a lot of rooves leak, if it is an apartment you still need to find out about the roof because it is often considered a communal charge. Best of all ask the neighbours - find out how the drainage is, if there has been flooding etc etc. Furniture is often included in the sale price - the houses on sale are usually summer homes and people don't want to pay shipping on stuff they already have. Buying things new in Turkey is expensive. Buying things second hand is very cheap, so bear that in mind when negotiating - you are doing each other a favour.
Note: it may seem like a good idea to ask the owner why they are leaving, you could do this I guess but people lie, especially if they are leaving because the sewage pipes keep overflowing. Neighbours are a much better bet, as is the previously mentioned calis beach forum - a lot of the members are long time residents / visitors to Turkey and have the gossip on all the different apartments and areas.
You might also want to call in people to check things individually - plumbing is frequently botched, electricity boards equally frequently have too-small fuses. This group is a good place to check to find people who can help with that and generally ask questions
Once you have seen a place, ask for a copy of the Tapu - house registration document / deeds - and take it along to the council offices to be vetted. Make sure the sellers name matches the name on the Tapu. Make sure the building has building permission. This is an ongoing cheat to both Turks and foreigners who buy houses which are illegal, you can still buy them, but they should cost a lot less. You should also bear in mind that it might be possible to get house building permission, but then again it might not be. It is extremely rare to be able to build a house larger than 25% of the land size, and usually it's 15%, if it is farm land it is never more than 10% and more likely 5%. Some land it will never be ok to build on. Some the people who live on the land have been paying taxes for it and living on it, but the land is not actually "residential," - what they are actually selling you is the right to have first refusal to buy the land when the government re-zones it to residential or tourist areas. It's dicey, but might be worth the risk if you are willing to accept that you might not be able to afford the land price later, and might lose your home at an unspecified point in the future (like paying all your rent in advance.) We considered a few properties along these lines but in the end went with a fully legal one. The land registration people will be able to tell you all the details about you house and the plot it stands on. They will also tell you if the house has a mortgage / bad debt - make sure this is paid off before you sign the land deeds or it could be transfered to you.
Another thing to check is the electric - ask to see a bill. There are several different types of electricity supply in Turkey - the two most prevalent are residential and construction. When you build a house you use construction electricity. This is more expensive. A property has to be converted to residential electricity with five years of completion. It costs a chunk of change to do so and if you don't you face a hefty fine. Note: if you do buy a property both your water and electric meters have to be purchased from and installed by the official water and electricity companies - this can be confusing as every hardware store sells them. They are not official, they are just to help people split up bills if they divide their houses, don't get caught out, the fines are astronomical, have something insane attached to them like a 500% interest rate and are just so not worth it!
Step 3 The haggle
If you want to haggle you need to study the market. Our budget was very tight, so properties we liked and could afford were not plentiful, it took us over a year to buy. The one we eventually got had been on the market the whole time I was searching, (and for a while before that) by the time we went to see it, the seller was very ready to drop his price. A lot of the properties are on the market for a very long time. There are a few reasons for this: sometimes people are just "trying their luck" - they don't really want to sell, but if they got their (outlandish) asking price they'd happily leave - sometimes they do and then all the prices in the area go up for a season or so before people realise it was just a fluke and come back to earth. Sometimes people got a bargain purchase and have put it straight back on the market at a higher price. There is one I keep seeing in the property pages at the moment, we looked at it when it was on for 90,000tl - someone bought it, did nothing, and it is back on for 150,000tl! But the main issue is the selling season is short, there is plenty of choice, but not plenty of customers. I don't think houses are a thing you should rush into, be honest about your last price and leave your number with the seller, they may well get back to you at the end of the summer if it hasn't sold and they are comfortable taking a lower price.
Step 4 The purchase
Note: this is not legal advice, I am not a lawyer, consider this a part of the extensive research you should do before committing any part of your savings to property investment.
From this point on for most everything you will need: passport photos (get a stash of 20 to keep you going,) a Turkish bank account, a Turkish tax number, your passport.
If you are foreign and want to buy a property in Turkey you have to have military clearance. This takes somewhere between six weeks and six months (sometimes longer, so far as I know never shorter.) This is also the only part I did through a real estate agent. They charged me 300tl to fill in the forms and process them. I used Apple Estate and have no complaints.
This is where things get tricksy - if you are Turkish you (obviously) don't have to get military clearance and the whole buying a house process can be done in a day. Really, just a day - once your clearance is through it will take one busy morning and you'll be all done. So if you buy from a Turkish person then having to wait an indefinite amount of time to close the deal and get the full house money can be irksome to say the least. Here is how we got around it. When we bought a house the owner had a mortgage on it (buyer beware - you can sell on a house with a mortgage, and the mortgage gets transferred too - the government has plans to change this but so far as I know it hasn't been done yet.) Anyway, he was especially anxious to pay off his mortgage (frightening 10% interest rate) - so we paid it off as our deposit. In return he gave us a cheque to the value of what we had paid. Cheques are different in Turkey to the UK, they are a legally binding contract. You get them individually from the bank and they have to be witnessed, if someone tries to cash one they can not be defaulted on without legal proceedings. He also gave us the house keys. We moved in and finished the process when my clearance came through. You might want to get a lawyer to hold the cheque for you (or the seller might want this) - ours trusted us not to cash it in.
You can of course go to a lawyer and get a contract drawn up instead stating what you are paying, at what stages, when you get to take possession of the house etc. We looked into this, the lawyer wanted 300tl, but the notary who would have to stamp the contract to make it official wanted 1500tl. We found the cheque method simpler - at the end of the day if the seller got a better offer and dumped us we were sure to get our money back. Him also giving us the keys was semi-unusual, he wasn't living in the property and didn't mind us going straight in. The seller knew he'd get the rest of his money because of course we couldn't get the land deeds without his signature - and he wouldn't sign anything unless he'd been paid.
I don't know the process in the UK, I think buying a house can take 3 months or so there anyway, so maybe a British seller would be more sympathetic to the military clearance issue. I don't know what kind of deposits people usually give in the UK either, I guess if you are both British you work out your own system of trust and security how you are used to.
So once your military clearance has come through the seller has to make an appointment at the Tapu office. You need to have dask in place before you go to this. Dask is compulsory earthquake insurance. Anywhere you see the word "SIGORTA" (insurance) will do it for you - the price is set by the government, currently around 110tl. So take that, your photos, passport, tax number and go to the appointment. The seller will be handing similar documents in to. You hang about while they process this and then they give you a form with a code for going to pay the property tax - around 4% of the registered price of your house. You do this at Ziraat bank - you can go in of use the special cash machine that accepts money. It is split between the buyer and the seller, the seller pays a little more. You get a receipt, return to the tapu office, hand it all in and half an hour later they are ready for you to sign stuff. In Fethiye you need a translator present for this - the office will give you a number of one of their registered people (an English speaking friend won't do, even if you speak Turkish, as I do, you still need a translator.) They read out the details of the sale - you should already know exactly what you are getting if you have thoroughly checked the Tapu - you say ok, sign your name, and they give you your land deeds.
Note - the amount you pay for your house may be different from the council-set price written on your tapu. This is normal. Ours was almost the same but that is unusual. If (heaven forbid) your house is destroyed by an earthquake your dask insurance only covers you up to the value of the amount on your tapu. If the price is really really different - you might want to do a bit more market research, these days the price shouldn't be that much lower. You have to get the current value from the land office - whatever is written on the current tapu is out of date within a year.
This was my experience and how we dealt with it - if you have more information, have done a blog post on the same subject please tell me / link it in the comments.