How to cook hamburger patty on the stove?

Alright, we have this meat guy, who comes by every so often and lets us buy meat. Now, some of the patties are in the fridge defrosting. I was thinking about cooking them on the stove, as I have no grill. How would I go about doing this? We have 4 patties, and I want to cook 2 for me, and 2 for my mom, and I don't want to screw it up.