If you are new to soldering, it is recommended that you check out iFixit's guide to soldering and desoldering.

Place the desoldering wick on top of the existing solder ball.

Hold the soldering iron in place until the solder melts into the wick.

Repeat the same procedure on the remaining connector.

Pull the desoldered wires off of the circuit board. They should come off with little to no resistance. If they do not come off easily, remove more solder from the contact points with the wick.