If you have been granted asylum (political asylum, refugee protection, subsidiary protection or suspension of deportation), you will receive a residence permit for a period of stay between one and three years. It will be noted in your residence permit if you're allowed to work. This isn't always the case, e.g. if you are under suspension of deportation.
If you received one of the first three kinds of protection, you are usually allowed to work without restrictions, including self-employment. If you are under suspension of deportation, the Immigration Office ("Ausländerbehörde") decides whether you are allowed to work or not.