Once the lock ring is removed, simply lift the old cartridge out. You may need to use some pliers since these can get stuck a little.
Now that you have it removed, it's time for a little trip to the hardware store to get a replacement cartridge. It's usually a good idea to bring the old faucet cartridge along as it makes finding a replacement a lot more fool proof. Sometimes the hardware store clerks just need to see the old one and can immediately show you where to find the replacement.
