Before you start soldering, it may be a good idea to check out the soldering and desoldering guide.

Melt the solder around the contact points with a soldering iron while using a de-soldering wick to absorb the melted solder.

Once the solder is removed from the contact points, pull the wires away from the circuit board contacts.

When attaching a new speaker, do not solder the two contact points together.