Place the wick on the solder connecting the speakers to the electrical board.

Place a heated soldering iron on the solder wick to melt the existing solder.

Pull the speakers off of the solder connection.

A solder vacuum can also be used in place of solder wick to remove old solder.

If you need more help with the soldering process, take a look at iFixit's guide for soldering and desoldering connections.