A panini press, or panini machine, is like a waffle iron, but the plates that get hot are flat or, more likely, ribbed, like a grill pan. You can buy one for as little as $40 or as much as $100.
The press is usually quite heavy for its size, as the top plate presses down on the sandwich, flattening it a bit and causing the sandwich contents to squish together and become one glorious, warm, melded interior.
Because both the top and bottom plates of the press get hot, the sandwich requires no turning and cooks evenly on both sides.
I use my panini machine to make every kind of sandwich, including good old-fashioned grilled cheese, but if you aren’t interested in cluttering up your counter with one more device, you can use a George Foreman-type grill to great effect in making hot sandwiches. Or you can use the method that short-order cooks have used for decades: Set the sandwich in an ordinary skillet to cook, but put a heavy pan or cast-iron skillet on top of it to press it down.