Silkworms are very easy to keep. Keep them dry and clean at about room temperature (70-80F) feed the fresh washed mulberry leaves or silkworm chow. Feed them as much as they can eat every day, don't worry about giving them water as they get water from their food. Don't need to do anything special till they get to abou 3" long and fat.
I keep my silkworms on coffee cup holders or egg cartons as this makes it easier to dump the poo and pick off shed skins without having a mesh of silk clinging to the worms. Also the creveces of egg carton and coffee cup holders give them a nice place to spin their coccoons.
Once the coccoon is done I transfer them into another container, lined with cut pieces of wax paper and put a cover over them. A critter keeper is great for this or any small rubbermaid container with holes or screen over top. It takes about 10-20 days for the moths to come out. They don't fly very well but its nice to have the lid on just in case they managed to get airborn. Once you have a pair of moths out, they typically will find each other and mate, if opposite sex (can't really tell males from females, other than in females their bodies are wider near towards the end and even that isn't 100%). Once they have paired off the males typicaly stay attached till the female is ready to lay eggs. If you have several moths and only one pair is bonded, chances are the rest are all males, especially if they keep trying to 'get' the female. You can feed these off to your bearded dragon as a treat.
Once the eggs are layed and have turned purple (a couple days after being laid this happens) remove them from the container and put them in the fridge. Leave them in the fridge for 3-4 months then take some out to hatch. Typically takes about 10-15 days before you can see little black worms coming out. Once you see the worms, use a fine cheese shredder to sprinkle some chow onto the worms or shredded mulberry leaves. It's realy hard to pick out excess food or poo at this time or even the worms so just leave them in, or even put a bit of chow an inch away from the worms and once they move away from the old stuff, remove it.
It takes a few weeks before you get one inch long silkworms so if you need a steady supply, you can start taking out more eggs once your last batch starts to get big enough to feed.