There is a tool for removing the cartridge
but I just put the handle back on and use it to
pull the cartridge out.
Note: Sometimes a cartridge will not come out no matter what you do, If this happens you may want to stop and call a professional
This happens more when you have very hard water. In a case like that it is best to stop before you damage the faucet, put the pin back in and go shopping for a new faucet