If your application for asylum has been accepted, i.e. you have been recognised as a refugee, or an individual entitled to asylum or subsidiary protection, you may work as an employee or a self-employed person without any restrictions. That means you have the same rights as a German citizen on the job market.
If your application for asylum has been rejected (check our chapter "Rejected Asylum"), but you have been granted a residence permit based on a national deportation ban, the immigration office will decide whether you can obtain a work permit. Check your residence permit or the additional papers given to you to see if you are allowed to work in Germany.