Trace any contact back to where there are some decent soldering pads. If there aren't any because the tracks lead under a black blob or something you'll have to scratch off the green solder mask with a sharp knife, taking care not to cut the track, and solder directly to the track itself.
The best way to do that is in exactly the same way as you'd solder to anything else. Scratch off slightly more track mask than you need, apply the iron tip to the track and then apply the solder to the track right next to the iron, or into the corner made by the iron tip and the board. The solder should flow onto the track just like it would anything else but it does take a bit of practice to get it right. Its not eay on thin tracks but it can be done.