Lizy, I agree with aromano. You may start by reading turkish newspapers online (Hurriyet, Radikal, Cumhuriyet) or try to read some articles in Turkish wikipedia (you may easily shift to English to understand the context of some articles).
If you decide to go for books, there are these children books called 'Küçük Ayşegül'. They are simple to read and there is a version in English called 'Mary'.
For poetry, I recommend the works of Can Yücel, Orhan Veli Kanık, Özdemir Asaf, Attila Ilhan. You may find some translations of Can Yücel works here -
http://lyricstranslate.com/en/can-yuecel-lyrics.html
I have also started by checking some songs, because it is not so hard to find their translations to English in the website enclosed above. I particularly enjoy Pinhanı, Bülent Ortaçgil, Birşen Tezer, Kazım Koyuncu, but you may choose other singers and bands according to your preferred music style.