Those who are new to soldering may want to check out iFixit's soldering technique guide. How To Solder and Desolder Connections.

Unsolder the 18 solder joints labeled in GREEN in the picture. Begin by heating up each solder joint on the motherboard.

When the solder melts and the wire is free from the motherboard, immediately lift the solder tip off the connection to avoid damage.

Due to the fragile nature of electronic components, it is important to limit the amount of heat transferred from the soldering iron to the motherboard. A simple way to accomplish this is to pull the wires with gentle continuous tension while the soldering iron heats up the connection.