A ten gallon aquarium seems to be the standard of measure that most people are familiar with. Ten to twenty adult millipedes can live in a cage this size. It's really much too large for most hobby species and the substrate to airspace ratio can cause it to dry out easily.
Various plastic shoe box or storage containers work well with millipedes. I prefer transparent ones so that I can monitor the contents without necessarily having to open it. You will want to choose the best size per the number of millipedes you are keeping and their size. If you end up with breeding pairs, you may want to increase substrate depth and container size.
Interestingly, portions of some millipedes' bodies fluoresce under blacklight. This is particularly common in polydesmid flat millipedes as seen in the video below. Polydesmids tend not to be great captives. They may need higher ventilation and a higher component of decaying wood from hardwood trees in their cages.
Ventilation: All pets that are being housed in containers need fresh air. A little bit of air flow goes a long way in preventing the kind of habitat that promotes the growth of mold and even small mites that occasionally infest food that is left too long in millipede cages. Ventilation is achieved simply by poking holes in a container or by cutting out a section of the lid and gluing a bit of plastic or metal screen over the opening. Millipedes do not need much ventilation though, and desiccation (drying out) is the most common cause of death in captivity. If you look at your millipedes once a week, you're probably changing the air enough for them in their tank to make even having holes in the container necessary. Of course, this is partly because many shoe box types of plastic containers are not quite air-tight anyway. It is often hard to recommend a perfect tank because so many will work and there are so many different options.
Humidity: Humidity is doubly important for pet bugs. Millipedes like to drink water and they need more than a bit of environmental humidity in their habitat when the time comes for them to shed their skin. Luckily, millipedes have fewer problems molting than most other bugs. Water is offered to millipedes in two common methods. A small, shallow water dish with the addition of a few pebbles will help prevent drowning. If you don't want to spend the couple bucks for a nice looking water dish, any upside-down lid will do. Alternatively, you can just pour water into one corner of the cage every few days which really lends a more natural look to the habitat than a plastic dish anyway. The substrate will absorb most of it, but your millipedes will still be able to drink from it and benefit from the humidity that it helps their habitat to maintain. Remember that the MOST common killer of pet millipedes is lack of humidity. The substrate should always be moist in the lower depths and at least slightly moist at the top. Millipedes can dry out overnight if, for example, you were to leave them in a glass bowl in open air. If your cage has a lot of ventilation (air holes), a simple solution is to take a sheet of wax paper and pinch it between the cage/container and lid as you put the lid on. You can thin put in a few pinholes if you are worried about lack of airflow, but again, this isn't usually an issue for a pet millipede whose cage is opened at least once per week or so.
Temperature: Room temperature is just find for raising all pet millipede species, whether nymphs or adults. As with most bugs, warmer temperatures and good food supply means faster growth though. Cold temperatures lower metabolism and the millipedes will grow much more slowly. Oregon Tylobolus sp. and some polydesmid flat millipedes do tend to prefer cooler than room temperatures.
Food: One of the really great conveniences about keeping millipedes as pets is how easy they are to feed. Millipedes are omnivores, so they eat pretty much anything and everything. Everything from fruits and vegetables to bits of dried pet food are eaten but these should all be considered supplements. One of the fun parts about keeping millipedes is that you can experiment with offering them leftovers from your dinner table. Yet, always remember that the primary diet of millipedes will be their substrate.
No millipede caresheet would be complete without some mention of Archispirostreptus gigas, the African Giant Black or AGB millipede. This once popular hobby species is nolonger imported into the US on account of the commensal (symbiotic) mites that live on them in their native habitat, and which proved to be damaging to certain agricultural crops in countries where they were imported as pets. Captive bred specimens occasionally surface in the US hobby, but this species was never a very good reproducer in captivity. They lived upwards of a decade and care was simple, but alas we speak of them mostly in the past tense now. Fortunately, captive bred specimens do not carry the commensal mites as this long dead specimen from my video below "naturally" did.
A millipede cage that is set up correctly in the beginning can be left alone for a month or more.