To make a patty melt, you'll need burger meat, of course, plus Swiss cheese, rye bread, and onions. You'll also need salt and pepper, butter for cooking the onions and bread, and brown sugar to sweeten up the onions.
While any ground beef will work in a patty melt, I like to purchase grass-fed, dry-aged ground beef to really bring in some flavor. I also prefer my onions deeply caramelized.
There's also a specific set of toppings typically used in a patty melt: The cheese is usually Swiss and sautéed onions may be considered de rigueur.