Problem: Burnt or Lifted Pad
The copper pad may lift off the PCB if you apply heat for too long (e.g., more than 4 seconds), or don't let the PCB cool down long enough before reheating a joint. This causes a disconnect between the component and the rest of the circuit.
This is one of the trickier problems to solve so take great care not to overheat your joints!
When this happens it's rarely worth the trouble to attempt a direct fix. Instead, a simple and more reliable workaround - though still tricky sometimes, especially for a beginner - is to forego using the pad and instead run a wire directly from the component to another place on the circuit board.
Start by visually following the copper traces on both sides of the board from your broken pad to see where they lead. The traces will be covered by a colored solder mask (like an epoxy) but you can still see them if you look carefully.
Any of the other solder joints to which these traces lead may be used. Solder a wire from your component to this other joint to work around the broken pad.
Ask for help: Since the specifics may vary from repair to repair, visit the support forum and post pictures to get detailed advice if this happens to you.