First and foremost, you're going to need wood! Campfires burn best when started with dry grass and leaves, then slowly built by adding dry sticks, and eventually, logs. Definitely avoid burning damp logs---these will smoke and ruin both your experience and your food. Also, try to avoid using woods with a naturally heavy scent, like cedar or mesquite. These will impart a flavor on your food, and it may not be a tasty one.
The best vessel for cooking on an open flame is cast iron. When seasoned (meaning, it has a thin film of grease on it so food won't stick), it's essentially impervious to heat, and provides a nice and even cooking surface. Even eggs won't stick to it! Be wary: do NOT use cooking implements with a "non-stick" chemical coating. The nonstick surface will emit harmful fumes if it reaches high temperatures. If you're in a pinch, head to the home store and buy a pre-seasoned cast iron vessel. It won't be perfect, but it'll be a lot better than a random skillet pulled from the cupboard.
Since camping is, at its core, an active pursuit, you'll want to eat a hearty breakfast to give you energy throughout the day. In a cast iron skillet or dutch oven, try making an omelet with plenty of eggs, sausage and cheese to stick to your ribs and fuel you through suppertime. If your fire has died down to just coals try this simple trick: layer the bottom of a paper bag with bacon, and crack an egg over top of the strips. Fold the top of the bag down securely, and then hold over hot coals. The bacon and eggs will cook inside the bag---it doesn't even require a skillet! If cooking eggs and meat over a fire seems too dicey for breakfast, just heat up some water and pour over instant oatmeal.
If you want something hot and more than just a PB&J in the woods, try these simpler dishes. Grab a few pieces of heavy-duty aluminum foil and load in ground beef, potatoes, and veggies. Seal up into a nice packet and submerge in the hot coals. If started right after breakfast, all of the ingredients will stew and cook as you go about your morning chores. By lunchtime, you'll have a great camper's stew to tide you over until dinner. Or, if you have a grill rack, place a few pieces of buttered bread on the grill, add some cheese, and have a smokey, gooey sandwich for lunch. This also works if you have a fork or stick with which you can suspend bread over the flames.
For supper, try the original grilled dinner: kabobs. With water-soaked bamboo skewers or metal skewers, load up any dinner item desired---including veggies, meat, and even tofu, and suspend (usually between two bricks or rocks, with the skewer acting as a bridge) over glowing coals. You can even grill fruit this way, and top vanilla ice cream with the carmelized treats. But if you want to go truly classic, just stick a few hot dogs on a stick, and roast away over roaring flames.