What is the best way to bake potatoes in embers?

It's actually pretty straight forward and fairly easy to do.

1. Build a fire. You are building a cooking fire, not a warm hands and look pretty fire. I use a log cabin style fire for this.
2. Wait for it to burn down so there are plenty of white coals. You don't want lots of "fire". Fire is pretty to look at, but more unpredictable to cook in then hot white coals.
3. While the fire is burning down, wash and prep your potatoes to bake as you would normally.
4. Wrap them tightly in tin foil.
5. Once the fire is burned down to hot, white coals, toss the potatoes directly onto the coals.
6. Wait until cooked (roughly 40 minutes for an average sized potato, on an average fire, adjust accordingly).
7. If you have a shovel or something, put some coals on to the actual potato as well, so you're completely surrounding it. It'll speed it up. If you don't have anything handy to handle coals, make sure you flip them half way.
8. Remove carefully and enjoy.

The moisture of a potato, will allow it to cook without burning. Just make sure you wrap them with no exposed areas, in order to trap the steam.

My family used to make these when car camping, it was fairly easy. We'd usually make the potatoes after the first day, this gave the advantage of controlling the heat of the earth somewhat due to the 1 day of camping prior to using the fire to bake stuff.

The main requisite is a mature fire, with lots of ash in a fairly thick layer and good coaling.

If using foil, we would coat the potatoes with oil or butter, thinly, wrap with foil tightly, and place in an area where coals were covered thickly with hot ash, then rake more ash over the top of the potatoes and cover that with coals. As the cooking progressed, the top coals would be renewed as needed, and all noses were on the lookout [err smellout?] for burned potato. For burning, potatoes were removed to a cooler spot, out of the coals, using only the radiant heat of the fire to finish cooking.

For potatoes au natural, the same procedure was followed, making sure the was no direct coal to potato contact. The results are mostly the same, the uncovered potatoes come out a bit dryer and the skin is not edible.

We would always cook lots and save the leftovers to make fried potatoes in the morning.

Another thing we would do, [this has nothing to do with your question, but is cool] especially when backpacking, was to take small plastic bags and put 1/2 cup/125 ml of Bisquick or some other self rising batter mix, a small box of raisins, and a square of foil, buttered on one side and folded up. At camp, we would take out the raisin box and foil, add water to the bag with the batter mix, squish it around until mixed, add in the raisins, squeeze the (thick) batter into the center of the foil, fold up the foil around the batter (leaving room for expansion) and bake the raisin muffin on the fire surround, using radiant heat to bake it.

I'm thinking of a bonfire that has been burning all afternoon - lots of wood, perhaps you've been cutting back a big hedge or a tree. I do this in winter. It's dark by 4-4:30pm. The bonfire dies down, but is still a large mound of smouldering embers. Leave it. Get on with something else.

Then go out and check the fire is OK (do this more often on a windy day). If it is glowing nicely, then this is the time for baked potatoes, baked onions and roast chestnuts. (The chestnuts need to be part of the planning. Don't do much planning - bonfires are for when the weather is just right - so I don't usually have chestnuts in.)

If you have really big, coarse-looking potatoes, use those. I agree with other postings above about timing - 40-45 minutes, if you are lucky in placing the potatoes (nicely covered, but not in a part where the fire is still flaring from time to time. "The moisture of a potato, will allow it to cook without burning" - usually.

Do something else now, or you'll be checking the potatoes too soon and spoiling their warm spot. So you'll probably be a bit late getting them out. Usually this is good - less edible potato, but more taste. The onions will now either be sweet and delicious or charred and bitter, or just burned away. All part of the fun. Some salt and butter are all you need. If the onions are OK (less likely), you don't need anything extra.

There are special purpose stove-top waterless clay potato cookers (or bakers), often referred to as a Kartoffel Teufel (potato devil). The preparation is extremely simple - just place the potatoes in the pot (without water) and on the stove and cook until tender. The taste is very similar to campfire.