Make a note of the polarity of the old capacitor, and mark the exact values you'll need for the replacement: capacitance and voltage/temperature ratings (these may be written on the part itself, or you can look up the part number).



Press the tip of a heated soldering iron directly onto the solder joint on the back of the circuit board that is holding the old capacitor down. Hold on to the capacitor itself with your other hand. As the joint melts, you can feel the tip of the iron fall into the hole of the circuit board. As soon as it does, pull that side's wire lead out of the board. Then repeat with the other side.



This can take a bit of trial and error. The goal is to dig the very tip of the iron into the joint so that the solder in the hole heats and melts. If there's too much solder for your iron to reach the hole itself, you may want to use a soldering wick to get rid of some of the excess.



Also, be aware that some manufacturers use solder that cannot be melted by a typical hobbyist soldering iron.