There are a number of people you can get to help you with your application - Ilknur/Rosie is one and you can read these posts to find others.
They can prepare your documentation and take whatever short cuts are possible and take the stress out of the process and thus are well worth it even if your Turkish is fluent
Basically you need to have rental papers or tapu - house documents and a paper from the admin office saying where you live.
Papers from a Turkish bank account to show you have sufficient funds to live here - this changes from time to time.
Alternatively proof that you have a pension being paid regularly into a local account can suffice I believe.
Photocopies of passport, a number of photographs - local photographers can do this easily,
A completed application form and the right file
Then you can have permission to stay in Turkey for one year and repeat the procedure in 12 months