In recent years it has become more difficult in Dortmund to find an affordable apartment that meets one's own needs. You can contact the Amt für Wohnen (Housing Office) if you are looking for an apartment and maybe you receive a suitable offer.
Of course, you can also go looking for it yourself. With a „Wohnberechtigungsschein“ (Housing Entitlement Certificate) you have access to low priced rental apartments. You can apply for this at the Amt für Wohnen. Under certain circumstances you are also entitled to housing benefit.
In different districts of the city, there is a Anlaufstelle lokal willkommen (Local Welcome Service Point), which can help you with problems and questions about your housing situation. The contact point also helps you to find your way around the new environment and arranges contacts.
The guide from "Planerladen e.V.", which comes in different languages, also gives helpful advice on looking for an apartment.
Don't forget to register in your city. Without registration, you will not receive any social benefits. If you move within the city, you will also have to change your registration. The Bürgerdienste International (Citizen Services International) is responsible for you.