Image Sourced Here
I need to update this with a photo of my own beetles over the weekend, but this one displays their various stages very well. Will also update with picture of dermestid mites.

Food

Dermestids can eat jerkied meat or fresh meat. Jerkied meats such as pigs ears, pig trotters and other assorted dog treats (unflavoured treats) are great starters while a colony is growing. Jerkied meats wont end up rotting and smelling. One important thing to remember is if your solely feeding jerkied meat to mist the enclosure every few days so they have water. Alternatively you can soak part of the jerkied meat so its moist. Be careful not to mist the enclosure too often, it should be dry again in under 12 hours to help stop mold growth in the tank.

One of the most important things I've found is not to overfeed them fresh foods - too much fresh meat will end up rotting and they wont eat once it becomes too putrid. Smaller portions until they can handle larger amounts are far better.

Once a colony has grown to a more significant size larger fresh meats can be put in and soon they'll be cleaning whole skulls and skeletons for you!

Housing

I've used plastic tubs - a friend has used a glass tank and my next enclosure will be a bar fridge on its back. They seem to thrive in any of these quite well, and even more so if you have a heater for them. One important thing to remember is if they get too cold they'll become sluggish, too hot and they'll die. I lost my last colony over a heatwave while the plastic tub was in the shed. The insulated bar fridge should help prevent this in future, but its a thing to be aware of if you keep them outdoors. Indoors be careful that none escape, they will consume natural material if they come across it. On the upside though they rarely fly so I've left the lid ajar if the tub ends up with a funk and been fine.
They are excellent climbers however - plastic tubs and glass they cant seem to climb, but be aware if you choose to store them in something else that they cant climb out before you leave them.

If you choose to heat your tank, an ideal temperature is between 20-25 degrees, above that and apparently they become prone to flying. Depending on your type of heater as well, some do need to be protected. I've heard that heat mats for reptiles are ideal, but absolutely must be put between two ceramic tiles and siliconed in with just the power cable sticking out - otherwise the beetles have a tendency to eat the heat mat.

Food care

If you feed them fresh bones - not jerkied, make sure to cut as much meat off of the skeleton before putting it in with them, unless you are sure they can handle the large quantity of meat.
For skulls I remove as much tissue as I can, eyes, tongue, brain when possible, cheek meat and any other I can get to. This also means they'll clean the parts much faster.
For full skeletons, same as above, just cut off as much as you can unless your sure they can handle it. No one wants to end up removing a half rotting carcass :P

One of the biggest things to watch for is maggots - I will never feed my bugs anything that might have maggots or eggs that might hatch. Maggots make the meat into this disgusting soup that dermestids will avoid, and its awful to clean up a tank when they're in there. Its much easier to just avoid them to begin with.

Depending on your country (Australia being the only one free of parasitic mites) dermestids can also get a parasitic mite that can destroy a colony. Searching on taxidermy.net for "Dermestid mites" will get you plenty of horror stories. There is a US product called "CheckMite+" that is used on bee colonies that will kill the mites, but not the dermestids if you do get an infestation. To prevent infestations make sure any beetles you introduce into, or start a colony with, are free of mites. Freeze any food for a few days to a week to kill any mites that might be on it (this includes wet or dry dog/cat food or treats!) and just keep an eye on them!

---

If you have any questions at all feel free to contact me or have a look on the forums at http://www.taxidermy.net under the skulls and skeletons section! I learned the majority of my knowledge from there, and the people there are usually quite helpful at answering questions.