Working from the edge opposite the battery connectors, insert a spudger between the battery and the plastic frame and pry up. The battery is attached to the casing with an adhesive, but should slowly come free.

We're now ready to begin the soldering process. You'll need a soldering iron, solder, and desoldering wick. You should be able to find these items at a Radio Shack if you don't already have them.

Clean the solding iron by melting a small amount of solder directly onto the soldering iron's tip and then wiping the tip of the soldering iron on a damp sponge.

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

Place the soldering iron on top of wick above the existing solder ball.

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

Repeat the same procedure on the remaining two connectors.

Lift the old battery out of the iPhone. Be sure that all the solder has been removed before pulling the wires away from the board. The wires should come free with little to no resistance.