Freie Universität Berlin offers (limited) support in finding accommodation, mainly rooms in student dorms or single apartments. Please have a look here and contact the Accommodation Office directly. Due to limited availability, accommodation is booked out quickly.
In Germany, it is very common to share apartments. In shared apartments (Wohngemeinschaft, WG) several people live together in one apartment, which means that each person has his or her own room (usually unfurnished) and the bathroom and the kitchen are shared. Shared apartments are mostly inhabited by young people and students. This is usually the least expensive accomodation option and the best way to meet people. Here are some online platforms where shared apartments are offered. They are also useful to find short-term furnished accommodation for the first weeks of your stay in Berlin: