Trim the leads of the new capacitor so that they are both even, and will sit at about the same height as the old capacitor.
Position the new capacitor leads at the holes where the old capacitor was, with the correct polarity. Just like before, press the tip of the soldering iron directly onto the joint in the back of the circuit board. As soon as the tip falls into the hole, press the wire lead through the hole, then remove the iron. The old solder joint will solidify around the new part and hold it secure. Repeat with the other side. Add new solder to the joint if necessary.