Here is how I keep mine. I have them in a LARGE container, rubbermaid. As large as you can do. They need space.
They enjoy hanging upside down on the underside of logs stacked overtop eachother, branches, pieces of wood, etc. They're an arboreal animal. They do need a waterdish to drink from, or need misted every few days.
I keep them in a opaque container so that they can receive some light. I keep the temps between 62F and 89F. A good average temp is around 77F. Humidity levels should be kept above 55% and below 95%. 75% humdity is a good average.
My juvenile D. diadema has been very easy to care for. He lives in a plastic enclosure with a large piece of styrofoam to climb on/hide behind (styrofoam is not the most attractive piece of furniture, but it's cheap and he can't injure himself on it). For substrate I use a wet paper towel, which I replace every several days. I mist the lower walls about every other day to keep the humidity up. He has molted several times and seems very healthy. If you're interested in amblypygids, check out Peter Weygoldt's book "Whip Spiders", which has a lot of in-depth biological information as well as a small section in the back about keeping them in captivity. They're a lot of fun to watch!