We feed our African Soft-furs the same diet as our mice: Mazuri Rodent Breeder 6F in addition to some fresh foods, seeds, and grains. There unfortunately isn't a lot of information available regarding their diet, but generally speaking, if it's safe for mice it's safe for ASF. You can find a list of safe/unsafe foods here.
ASF should always have access to fresh water from a water bottle or dish.
There are many great options for bedding available, but like with all pet rodents you want to make sure their bedding is as dust free as possible. We use paper bedding, but aspen or kiln-dried pine shavings would also work. No cedar or non kiln-dried pine. We have found that our ASF don't seem to burrow as much as our Mice do, but we always make sure their bedding is thick enough they have room to burrow if they choose.
African Soft-furs love to run on wheels. We also provide food enrichment in the form of millet and oat sprays (usually available in the bird section) to encourage them to forage.
As with mice, we find most commercially available cages to be inadequate. They're usually either too small or too flimsy. We use bin cages for our ASF, which you can see here.
Being relatively new to the pet hobby, ASF are usually not as friendly as mice or rats. Ours have been bred for temperament and we find that with regular interactions they will allow us to pet them and not try to bite. They do not enjoy being picked up, however. If you're looking for a pet to snuggle with, ASF are probably not the right choice for you.
There are limited resources available on these animals, but we have included a couple of links here.