My aunt used to cook them for us quite often.She used to do them in the oven like you do a roast.She would put potatoes and carrots and onions in with.I love eating groundhog I haven't thought about cooking one in a long time since she passed away.Now I think I'm going to cook one for myself.I hope this helps.
Hubby's mother use to cut them up like chicken, squirrel or rabbit and pressure cook them. Then season with flour, salt and pepper and fry like chicken.
I've never eaten one but DH and his family grew up hunting groundhog just like any other wild game.