OK, I fixed my link, and as I predicted, hj has already identified the faucet for you. As he says, that metal handle insert is only "stuck on" by the friction and possible mineral build up over the ages. Wiggling will usually do it.
After you get that off, the obong chrome flange will just unscrew. It is screwed onto a plastic nipple around the long stem. It may be stuck in place with caulking. If so, carefully use a thin putty knife to slice in under it to break the bead. Finall, after turning off the water, you can use a special shower socket to unscrew the stem for replacement. Remember to replace the internal seat, which also unscrews out of the valve body.
TIP: When removing and reinstalling the stems, always turn to partly on postion. DO NOT try to wrench them when they are fully closed.
All the parts for this are readily available both individually, and in complete repair kits. Genuine PP brand parts are recommended. They will run about $75, vs. about 1/2 that for a generic, but will probalby last twice as long and be more reliable