you can just hop on the trams and buses but if the inspectors arrive they come in force, and it is very hard to slip away.
go and ask in the occupied school Denk:mal (Lagerweg) or alternatively in the Reitschule (just before Lorrainebrücke, you can't miss that one). The only problem with the Reitschule ist that it is not always open. Update July 2016: Reitschıle is closed now, and as I heard, it will be closed until August 2016
Also you can camp in the Stadt Nomaden or stay in someone's caravan if you ask for a couple days. It is located in Studerstein (a park) Directions: once you reach the park you can ask this name. It is a little area bordered with fences, where there are caravans and many dogs. To come to the park, you can take the bus 11 direction Neufeld from around the city centre and get off at the last station. There you will see the Studerstein and the forest, don’t go into the forest :)
you don't need a permit. but the competition is pretty intense and almost all the streets have cars so there are very few great spots for the un-amplified buskers. but according to some you can earn 50-100 francs in an hour or two. according to others you can expect more like 10-40 in a couple of hours.