The application for this scholarship is little more complicated, it actually takes some hours. I advice you that you scan all of the documents you need (if I recall correctly, they only accept scanned document in .jpg or .doc format). The application has also a part where you need to write your motivation for scholarship. Recommendation letters are not necessery but can be an advantage.
At the postgraduate level you can choose maximum 12 universities and minimum 3 universities and departements. So before you apply for the scholarship, check web pages of more universities and their programmes, because, as it's written on the official page of Turkiye burslari
''selecting more cities might increase your chance to get scholarship''.
The application for the scholarship opens online (on the official page). Before you do it, read instructions carefully. Don't wait until last day, because last year there were some techincal problems on the page, and in that case you might not be able to send your application. If you have some problems when applying, you can get assistance from Turkiye burslari.
After applying (which was in 2013 in March), we waited almost 2 months for the ressults of first assesement. If your application is good enough, the Turkish Embassy from your country will call you for an interview. The interview dates depend from country to country. Mine was at the end of May. After interview there comes again waiting period. The final results were released at the end of June, however, at that time we only got to know, if we received scholarship. The news about university we won came in the late July/ early August.
After the results we had to bring original papers (the one we already attached with our application in March) to the Turkish Embassy in our country. To be able to sign a contract I needed the copy of passport, graduaton paper (it doesn't need to be original), health report and the paper that Türkiye burslari sent me, which prooved that I won scholarship. The Türkiye burslari group also send a scholarship contract to our embassy. We had about 2 weeks to go to embassy, bring all papers (in English or Turkish) and sign the contract. At the same time also the procedure for student visa started.
Some embassies don't have many experience with scholarship, so my advice is, to read the rules (sent to you by Türkiye burslari comitee) carefully and also take one copy with you to the embassy. Sometimes they receive the scholarship contract little late, so be patient. If you won scholarship, probably you will visit the embassy few times, before you will arrange everything.
After this step, again come waiting and patience. Now you only need to wait, that scholarship team sends you flight ticket. For us it was kind od surprise, because nobody really knew, when will we travel to Turkey. Finally, we travelled to Turkey in second half of September and some even in first half of October. The scholarship team bought us ticket from the closes aiport (where Turkish airlines flies). Some students had to buy conecting flights in case that Turkish airlines doesn't fly to their country. They had to buy it on their own, but latter they reimbursed this money to them (this latter means few months later, so don't rely on getting that money soon).
For more information about the selection and interview process check
Study in Turkey#2.
Undergraduate scholarship
The application and assesement process is similar to the one described above. The important difference is the time for application, which was in 2013 in May, however, check the official page of Türkiye burslari for the application dates in 2014.
Other important difference is, that undergraduate students to be must choose 12 different universities where they want to study and olny 6 of this universities can be located in Istanbul, Ankara or Izmir. This means, if you will win a scholarship maybe you will not be placed in one of the big cities.