I go camping a lot and I'm always in charge of the food. It's amazing how many people are completely clueless when it comes to cooking on an open fire.
There's many ways to cook on a fire, a lot are survivalist ways but I'll be going over methods for people who want to have a hearty meal while camping with some friends.
If you have meats that are still frozen or drinks that need to be cooled, find a spot in a river that has a decent current(you don't want stagnant water filled with bacteria on your beer cans) and create a barrier of rocks to keep it contained. The river is now your refrigerator and sometimes in the early morning and it can be a freezer.
For grilling I suggest getting a portable grilling screen preferably with legs.
I have one like this but it's more light weight and more portable.
If you don't have one with legs yank the screen from your grill or go buy one from walmart or your local grocery store, they have specials ones at my Martins that has a lip on it so food doesn't roll off. They're very cheap, no more than 5-6 bucks.
When I camp I have a large campfire pit that I use through out the night for light, heat and smoke to keep bugs away, next to it I create a smaller circle of rocks solely for cooking. It should be small enough to fit under your grill screens legs, if you have a normal legless grill screen, set the screen on the rocks and make sure it's 100 percent sturdy, you don't want to get 90 percent through your meal and then lose it. With this screen you can cook nearly anything you put your mind too, boil water and dry out wet clothing.
Don't set the screen on the logs, logs roll and most importantly they burn!