How do you cope with an asymmetric flap extension?
I'd guess the procedures probably vary considerably by class and type. If the flaps on one side broke or got stuck on the light GA plane I mostly fly, the procedure would be to just set the side you can control to the same as the side you can't control and land with that amount of flaps. You can land it with no flaps; you'll just have to land a little faster than normal and with sub-optimal visibility of the runway (but still plenty to get the plane onto it safely.)

At least in the planes I've flown, it would be nearly impossible for the flaps on both sides to get stuck in different positions (because both sides are mechanically connected to the flap lever,) but even that could be dealt with by using the ailerons to counter the asymmetry of lift.

The other procedure involved is to do a proper pre-flight and make sure your flaps aren't broken, loose, or damaged before you leave the ground. :)