Greenstuff has it mostly correct. This is a Roman classic, leave out the garlic though. Guanciale (from pork jowl) which is hard to find here (but not impossible) or pancetta. Pecorino would be the preferred cheese. Butter yes.Cream no. Plenty of ground black pepper. The steaming hot pasta does cook the eggs. Figure three eggs to 12 ounces of dried pasta.

I don't think of carbonara as a sauce as much as I think of it as a method. Basically, you cook some bacon or pancetta with a little garlic and maybe a splash of dry white wine. Set it aside. You mix about 3 eggs with some grated Parmesan and maybe some pecorino romano. You cook a pound of spaghetti, drain it, and IMMEDIATELY toss it with the eggs and cheese so that the warm pasta cooks the eggs. Toss it with the bacon and a little parsley.

Nigella Lawson has an easy one that is my go-to dinner. Basically, render about 4 oz of bacon/pancetta/proscuitto in a bit of olive oil in one pan as you cook your pasta. Once the bacon is crisp, add a 1/4 C white wine (optional) and let that bubble for about 5 minutes or so. Right before the pasta is ready, add one (or more) tablespoons butter to the hot bacon pan.
Mix together in a small bowl one egg plus one egg yolk with 1/4 C (or more) parm. cheese, salt, pepper, and nutmeg. When the pasta's done, drain and then add to the hot bacon pan and toss over the heat until coated. Once that's done, remove the pan from the heat and add the egg mixture, carefully and continually stirring until the pasta's coated. Serve right away.
You can also add frozen (or I suppose fresh) peas or broccoli to the pasta as it's boiling.

I haven't tried this recipe, but it looks like a good one:

http://allrecipes.com/Recipe/Spaghetti-Carbonara-II/Detail.aspx