I know that a LOT of people have shared a "rule of thumb" for calculating the number of briquettes to use on the bottom/top of a dutch oven to get a temperature of around 350 degrees.  The rule of thumb is to take the size of the oven, subtract two coals and put that many under the oven.  Add two coals and put that many on top of the oven.  So a 12-inch dutch oven would have 10 briquettes underneath and 14 briquettes on top.

I found that this works VERY well--if you have a 12-inch dutch oven.  When I use this rule of thumb with a 10-inch oven, it's quite a bit hotter than a 12-inch oven.  When I use it with a 14-inch oven, it's quite a bit cooler than a 12-inch oven.  This became quite clear when I made giant cinnamon rolls in my ovens yesterday.  I made a dozen, and they were so big, only 8 of them fit in my 14-inch oven, so I put the other 4 in my 10-inch oven.  Using this rule of thumb, the rolls in the 10-inch oven were done a LOT quicker than the rolls in the 14-inch oven.

I used to tell people this rule of thumb when all I had was a pair of 12-inch lodge logic ovens.  But now that I have a 10 and a 14, I'm trying to figure out how to REALLY know how hot the oven is inside.

How do you cook in larger/smaller-than-12-inch ovens?

Here is an excerpt on temperature control from a hand-out that I use when teaching Dutch oven classes...

Temperature Control
 
On my dutch oven, there's no dial, nothing to tell me how hot the oven is. Since cooking food at a fairly consistent and known temperature is important for success, there are 3 ways I know of for estimating temperature. Depending on your skill level and how you'll be cooking, one of them should work for you.
Also keep in mind that there are many environmental factors that will influence your oven temperature. Wind might blow heat away; colder air temperature, higher humidity and higher elevation reduce heat generated by coals; direct sunlight makes a black oven a bit hotter. You might consider making an aluminum foil wind shield to place around your oven, but if it is that windy, I would recommend you not have an open fire.
Nearly all dutch oven cooking will come out ok if your dutch oven is about 350 degrees.

Hand Test

Use your hand to feel the heat. Of course, every person has a different sensitivity to heat but this works well for me. Just remove the lid from the dutch oven and place your hand just above or just inside the oven. Count how many seconds you can keep your hand there before it gets too hot. It is about 50 degrees per second counting down from 550, so I just count - "550, and 500, and 450, and 400, and 350, and 300, ...".
Seconds Temperature
1 500+
2 500
3 450
4 400
5 350
6 300
7 250
8 200
This is a pretty good method. It is consistent and detects temperature instead of estimating the amount of fuel. You do release heat so you need to do the check as quickly as you can.

 
Counting Charcoal

Lots of dutch oven cookbooks tell you how many charcoal briquettes to put under and on top of the oven. This is the easiest way to cook since every coal is similar and consistent. Different brands of charcoal give off different amounts of heat, as does wood coals.
The normal formula is to use twice the number of briquettes as the diameter of the oven. For a 12 inch oven, you would use 24 briquettes. Depending on the type of cooking you are doing, you need to make the heat come more from the top or bottom of the oven. For example, too much heat on the bottom will burn bread.
To do this, you place more or less of the briquettes on the lid.
Here is a simple chart:

Baking More heat from top so bottom does not burn.
Place 3/4 coals on top and 1/4 underneath.
Roasting Heat comes equally from top and bottom.
Place 1/2 coals on top and 1/2 underneath.
Stewing, Simmering Most heat from bottom.
Place 1/4 coals on top and 3/4 underneath.
Frying, Boiling All heat from bottom.
Place all coals underneath.

Rule of 3

This is a real simple estimate of briquettes. Take the dutch oven diameter and add 3 briquettes on top. Subtract 3 briquettes underneath. So, a 12 inch oven would have 12+3=15 on top and 12-3=9 underneath. This works for most any size dutch oven. Then you need to adjust briquette placement depending on the type of cooking.
 
Rings of Coals

As it turns out, the sizes of briquettes work out so that the recommended briquettes count above can be estimated easily. As an experiment, you can take a 12 inch dutch oven and 24 briquettes. On the lid, make a ring of briquettes all the way around the outer edge. How many did you use? I bet it was 15 or 16!
Now, see how many it takes to make a ring just under the oven. There should be 3 or 4 briquettes between each leg for a total of 9 to 12.
That is pretty close to the recommendation for a 350 degree roasting set up, isn't it? It works pretty well for any size dutch oven and any size briquettes - smaller briquettes means you need more of them, but its about the same amount of burning mass to make a ring!
A ring around the top and the bottom is about 325 to 350 degrees.
Remove every other briquette underneath to make 300 degrees.
Add a second ring to the top to make 375 degrees.
If your camp cooking calls for stewing or frying, you'll want to drop most of those top coals down and shove them under the oven. If you're baking breads, then maybe move a couple from underneath up to the top.
Just remember that a ring around the top and a ring around the bottom is your base starting point and tweak it from there.

Temperature Tips

Finally, just a few tips to tuck away for later:
• You can cook food, but you can't unburn food. Use less heat and cook longer rather than overheating.
• Preheat your dutch oven for frying or searing meat. Otherwise, put the food in cold and let it all heat up together.
• “If it smells done, it’s done…If it smells burnt; it’s burnt…If you can’t smell anything it isn’t done yet.”