The Studienkolleg does not offer housing for the students.
A very detailed overview about the possibilities is published on the websites of the International Student Counseling. 
As soon as you are an officially enrolled student you can apply for housing at studierendenWERK BERLIN 
The linked Websites of studierendenWERK BELRLIN include information regarding their own dormitories and about many other possibilities to find something suitable.
From now on the InfoCenter IC studi@home will be available for all inquiries concerning living.
Monday to Friday
10 a.m. to 5 p.m.
You can also send your inquiries by e-mail at firstname.lastname@example.org  or contact them by phone, dial 030 93939-8990.
Shared / Own Flat
Another good and reasonable priced way of living is to share an apartment. You can find offers for that on many websites, for example on www.wg-gesucht.de  or www.studenten-wg.de 
Especially at the beginning of a new semester, many students are
searching for a room or flat. Make sure to apply for many