This is the repair that really drove home the meaning of "retaining clip." This repair also fulfills my advice to "talk about your mistakes."
The shower hadn't been used in more than ten years, so I wasn't surprised to find the faucet knob frozen. I turned off the water, went to the shower, and pulled off the cap, unscrewed the screw holding the knob on, pulled up and out on the retaining clip, and grabbed the valve stem with a pair of pliers. (Actually, they are Channel Lock adjustable pliers, what used to be called water pump pliers.)
That was mistake #1. After some twisting and yanking, I pulled out what I thought was the valve core and headed off to Home Depot to find a match. Mistake #1 was remedied by the helpful HD guy, who told me the part I was going to buy was wrong because I had removed only the central core of the valve stem. He gave me the right part and I returned to the shower.
Key Item: In the package with the new valve stem is a nylon tool that fits in the notches of the outer valve core. Put it on and then use the pliers to rotate the entire valve core so that it loosens enough to pull out.
I installed the new valve core (or stem) into the valve after slathering it with silicone grease and replaced the retaining clip. But now the metal cylinder that is supposed to slide over the valve body wouldn't. The top of the retaining clip was sticking up too high. Examination of said clip revealed that it was kind of bent and wouldn't go all the way down. A search of the Home Depot and Lowe's web sites revealed that it was not a stock item. Mail order only.
Mistake #2. I was about to order, grumbling at the $4 to $5 shipping charge on top of a $4 to $8 charge for the clip, when my wife, who isn't much for tools, suggested I try a plumbing supply house. "OK Google" found one only a couple of miles from home.
It was a few days before I could return to the repair site with my nifty, new retaining clip, so of course I had turned the water on again in the meantime. (You can see where this is leading to Mistake #3, can't you?) So I step into the shower stall, grab my needle nose pliers, and yank out that bent old retaining clip. In a quite surprising demonstration of the retaining clip's name and purpose, the entire valve core instantly shot out of the valve body, followed by a fire-hose-like stream of water, aimed directly at my chest. For an old guy of 66, I'm not kidding that I dashed out of the shower, down the hall, through the entry way, out the front door and to the shut off valve for the house.
Cut to the chase. The valve core went back in, the new retaining clip slid all the way down, water turned back on, and all is right with the world.
Installation secret #1: Be sure to push the valve core all the way in so that the retaining clip can slide down. Twist the core to line it up so the clip slides in the grooves on the core
Installation secret #2: To be sure that twisting the knob left makes the water hotter and right colder, make sure the little tab on the knob stem part of the valve is facing up. If not, rotate it up.
Maybe the best idea is to get the whole kit at one time: