Previously, CowboyCurtis asked for information about dutch oven cooking. Early emigrant Annie Taylor Dee remembered of her experience on the trail, "Most people cooked in camp kettles." Some settlers such as "Mrs. Lorenzo Roundy" in Kanarraville continued cooking directly on the coals well after the arrival of the railroad. In a previous query someone asked how the arrival of the railroad might have impacted foodways in Utah. Most directly, the railroad made it cheaper to buy a cook stove, because the freight issue on cast iron became more affordable. Even so, Patty Sessions brought a cook stove with her in the vangard company of 1847.
So then, having established that most people cooked directly on the coals (i.e. hearth cooking) before 1870, let's draw out what that means. Hearth cooking usually happens at ground level, so cooking utensils (such as lid lifters, coal shovels, spoons & spatulas)tend to have longer handles-- this as an effort to eliminate stooping. Think of your common fireplace set with its poker, tonges, shovel, and broom. Also the cooking pots must have legs to situate themselves on the coals. Legs are either cast directly into the construction of the pot, or pots can be set on a trivet or spider. And of course some pots were suspended from tripods or cranes. A crane is an L-shaped bracket on hinges mounted into the masonry of a fireplace so that suspended pots can be easily rotated into and out of the fire.
So much of cooking (as with any other pursuit in life, such as carpentry or bicycle mechanics) is a matter of having the right tool for the job. Count how many kitchen utensils and implements you have in your kitchen-- dutch oven cookery requires similar (though uniquely adapted) tools. And just as some chefs get by with one crappy knife and a terrible pan, some early Mormon hearth chefs got by with just one frying pan and no dutch oven.
As for the cooking part, most elements there are the same as cooking on a stove top. It all comes down to careful regulation of heat. In modern day dutch oven competitions, people cook just about anything you'd find in a fine French or Italian restauraunt. Some dishes call for frying, others for stewing and yet others for baking. All of these operations are done with the same pot (or multiple incarnations of the pot), but with different approaches to heat regulation. More coals equals more heat. Closer to the coals equals hotter. For beginners, try experimenting with frying bacon and not burning it to a scorched crumble. This takes patience on a moderate heat. Like many beginning stove-top chefs, too much heat is the beginning dutch oven chef's common mistake. When you can do this reliably without a lot of hassle, then you might step up to stewing. A long slow simmer without burning to the bottom takes a bit more effort. Baking is most tricky as it requires hot coals on the lid as well as underneath. Modern competition chefs use a formula of charcoal briquettes for establishing precise temperatures; historic chefs used coals from burning logs and did it by gut feel. I prefer to cook with wood rather than charcoal briquettes. They just seem so artificial. If you want to get really fancy you might try chunk charcoal, still in wood form (not compressed).
Well, there's the quick and dirty for you. Don't burn yourself!