Finding accomodation in Tübingen might not be easy, especially in October when the majority of new students is looking for a place to stay. We therefore strongly advice you to apply for a room in one of the student's dormitories.
You will find an overview of all the available halls of residence in Tübingen on the website of the Student Union Tübingen-Hohenheim following this link.
If you decide that you want to apply for a room in one of the dormitories, you can do so by filling out the online application which can also be found on the website of the Student Union Tübingen-Hohenheim.
The application deadline for the winter term is May, 31st, for the summer term it's December, 31st!