Turn water supply OFF to shower valve or entire house.
Open valve to relieve pressure. Pull horseshoe clip up and out
(I use a pair of needlenose pliers)
Then pull cartridge forward and out.
Since very old, probably best to go to a local plumbing supply house and get an older model MOEN cartridge
Grab a little silicone grease to grease up the o-ring on new cartridge and install the cartridge in reverse order.
If you have problem removing the stem after you have removed the horseshoe clip then you can try re-attaching the handle and give a yank with that OR you may need to purchase a cartridge puller
at the supply house when you get there! These cartridges can be tough to remove without the puller, but it can be done with a good YANK... most of the time (be careful not to YANK too hard...
PS: If hot and cold end up reversed after you fix this just rotate the cartridge 180 degrees and re-install the handle!
Let me know how it goes...