Please, I would like to know if someone here can give me some information about small places to rent in Istanbul and if you guys know in which distric I can find such a things and if there are so many burocracies to make an contract and of course how much it normally may coast.

Thank you all for the answers!

many such places rent small flats. As a foreigner, I'm guessing you want to be near Sultan Ahmet or Taksim. Lots of Real Estate people to assist you. Keep in mind, they charge a "finder's fee" of 1 months rent.
Good luck.

If u dont mind staying on the Asian side of Istanbul, I recommend u to come to Ümraniye U can find many small places and cheaper than most districts. We even have Japanese and Africans living here Prices can change from 350 Liras to 750 liras monthly.

Take a look at this

http://www.merhabaforums.com/classifieds-f82/central-kadikoy-spacious-apt-t5870.html