Heat the wire connection's solder joint until the joint looks wet and liquidy.

While maintaining contact with the solder iron, free the wire end by pulling the wire away from the board with the tweezers.

For instructions on how to solder properly please refer to this soldering technique guide. How To Solder and Desolder Connections

Remember which cables were soldered onto where. You will have to re-solder the cables back onto the same joint.

Solder iron is extremely hot and should be handled with care. Always wear eye protection when soldering.