First, answer the questions in the online app on the website of the „Charite“ hospital in Berlin (German and English only):
https://covapp.charite.de/disclaimer
If the result says that you are possibly at risk of being infected, get yourself tested!
If possible, call here before the test (and not the Berlin 030-phone number in the online app!):
Corona-Hotline-Phone of Landratsamt Tübingen: 07071 207-3600
You can call daily from 8 a.m. until 6 p.m.
There is a Corona-Test-Station at the Festplatz in Tübingen (behind the Freibad/open-air swimming pool). Examinations for infections with the coronavirus are possible there at the following times:
Monday-Friday: from 10 a.m. until 12 a.m. and from 4 p.m. until 6 p.m.
Saturday: from 10 a.m. until 12 a.m.
Waiting times until it is your turn to get tested are very long (several hours). After the test you will have to wait for several days until you get a result. Please only go there if you are quite sure that you may be infected
Here is more information from the Landratsamt, unfortunately only in German