Start at the top and pull the leather away from the wood. Same when you get down to the handle wrap. If you need to soften the glue a little, soak in a little denatured alcohol from the back/rough side of the strike plate. Use denatured alcohol to clean up the glue residue as well. That's if the glue used was contact/barge cement. Some glues don't come off that easy.
To install the new one, just do it in reverse. Push the lower end (with some contact cement on it) under the grip wrap and then affix the rest of it in place. May need a thin butter knife or popsicle stick to push the leather under the wrap. Good luck.