Generally a stem is extracted this way:
0. Turn off the water!!!! If it is just the hot side you are working on that can usually be turned off separately at the hot water heater.
1. Take off the handle.
2. There is a sort of metal ring around the post that went into the handle. It unscrews, but you may need a strap wrench to get it moving. Don't use a plumbing wrench - even if you tape that ring really well the wrench's teeth will rip up the finish.
3. After the ring is off the flat plate like piece (sconce?) which is against the wall should come off. These are not threaded onto anything, they are held in place by the ring.
4. Now you should see a big nut which holds the stem in place. Remove the nut with the appropriate plumber's socket.
5. Pull out the stem.
If your house is old and has rusty pipes a big slug of rust can sometimes build up just upstream of the hot or cold valve resulting in a low flow condition on one side like what you describe. If that is what it is, after the stem is out turn the water on briefly and it will probably blow out the plug of rust.
