This is one of my favorite comfort foods on a lazy day, or when i am enjoying a hot bowl of soup on a cold winter day. If I remember right it is the first thing i learned to cook at about the age of 9.
I will give you a basic recipe and then a couple of ways to add a little zing to them.
The basic recipe:
2 slices Cheddar, American, or Swiss cheese ( you can use just about any cheese but these melt the best and seem to be the preferred cheeses)
2 slices white bread (or your favorite)
2 tablespoons butter
Preparation
Put the cheese between the slices of bread. Heat 1 tablespoon of the butter in a skillet or grill and when melted add the sandwich. Gently press down with a spatula once or twice during the grilling. When one side is golden, add the remaining tablespoon of butter, turn the sandwich over, and brown. (some people like to spread the butter on the bread first, but the method above is a lot less messier)
Then if you want to get creative, you can dress them up a bit.
Grilled Cheese with Bacon. Fry 3 slices bacon until cooked but not crisp. Pat dry of excess fat, add on top of the cheese, and grill as directed.
Grilled Cheese with Ham. Put 2 thin slices ham on the cheese and grill as directed.
Onion-Cheese Sandwich. Follow the recipe for Grilled Cheese Sandwich, but lightly coat 1 slice of bread with Dijon mustard. Sauté 3 to 4 slices onion in butter and put on top of the cheese. Cover and grill.
Tomato-Cheese Sandwich. Follow the recipe for Grilled Cheese Sandwich, but add two thin slices tomato to the sandwich before grilling. You can add bacon to this one also. Oh what a treat.
I have a friend from Hawaii that likes to add fried spam to his grilled cheese and actually it is very tasty.
Well now that I gave you these recipes, I have worked up quite the hunger. Think i will go make me a grilled cheese sandwich or two 
Good luck and best wishes.