How many hours after a dental filling should I wait before brushing my teeth?

None. You may brush your teeth as soon as you want.
Zero. You can brush right away without hurting the filling. But, you might want to wait until the numbness wears off, so you don't hurt the tissue or make a mess.
Depends. This depends on the type of filling. Most composite or white fillings can be brushed immediately. Silver amalgam fillings need to wait for at least 3-5 hours before they set completely.