Before you jump in and expect everything match your needs perfectly, you need to do a little research yourself:

-What are the airports you plan to depart / arrive to and from?
-What airlines operate the route(s) you are looking for?
-What alliances are those airlines a part of and what are their award requirements?
-What are the mile requirements for your desired class of travel (Economy, Business, First Class, etc.)?

As the previous posters have mentioned already, the easiest way in a short amount of time is to take advantage of the credit card mile offers available now. If it's Turkish Airways you're aiming to fly, it looks like you would need to accumulate points on a Star Alliance partner airline (United, Continental, etc.) and do a partner airline award redemption. As such, you would need to look for mileage on one of those specific airlines and basically put all your spending on it while looking for any other bonus mile offers to add to your miles.

One other thing to check - not every flight will have award seat availability, so even if you have enough miles, the flights you want may not even have award seats to cash in on. So you also need to be flexible with dates as well.

The two blogs referenced are great starting points - but the forums here can also help you with additional specific offers for each frequent flyer program.

Good luck!