I'll add the same warning I have done a few times lately.
Please don't remove the cartridge unless you have to. FYI, you do it by loosening the tiny screw on the top of the headshell, and then moving the handle back about 45 degrees. The cartridge will then almost drop off, but what people often do is force it back or, more likely, force the lever forward when the cartridge is being reinstalled but not held up against the shell properly. There are hook-like tabs on the top of the cartridge body that will easily break if you don't do this right. Replacement cartridges are rare and expensive usually.
Replacing the stylus however is easy enough without doing this as of course it will slide off. Get a good grip on the silver cartridge body when you do this as sometimes the old glue that holds the silver part into the black plastic portion will fail. That can be re-glued so is not that much cause for panic but better that it not happen at all.