I've taken a screenprinting course and was pretty ok doing it. The book I have is "Screenprinting: The complete water-based system" Water based is best for the house so you don't have to worry about ventilation and harmful chemicals. For supplies, I'd recommend Dick Blick, the website is dickblick.com. They're not the cheapest but I've had a lot of good orders from there. For a basic website: http://www.moma.org/exhibitions/2001/whatisaprint/flash.html
The basics to setting it up, you'll need 2 table clamps, a screen, squeegee, ink. This allows you to lift and raise your screen while keeping your registration. A tip I know is to tape a dime on each corner, on the end closest to you, away from the clamps. It helps lift the screen off the table a little more and it helps to get a crisper image, in my experience.
To put your design on a screen, there are two ways I know. Using contact paper and using a photographic method. But that requires an exposure unit and not quite worth it for the house. With the contact paper, it's not a permanent method, you won't hurt your screen in anyways. However, it will be hard to get many *good* prints. The ink can go under the cut edges some, so if it's really important make multiple copies.
So if you have your design on the screen, clamped in, paper on the table, put the screen down. put ink at the top, put your squeegee in the ink, use 2 hands use firm pressure and pull towards you. Not slow, but not too fast. When you get all the way over, pop up the screen and do what is called a flood pass. It is where you take ink from closest to you and go back towards the top. It keeps it from drying out. Dry ink in the screen is a bad thing because it will affect your print in a bad way.
If this isn't enough details, let me know. Or if it's confusing, ask questions I'll explain better. I hope it helps.
There are various fabrics you can substitute for real silk when "silk screening." In fact, the whole technique is called "screen printing" these days because silk is no longer often used... instead, a fine *polyester* mesh fabric is used (although various open-weave fabrics can be used for various effects).
You can buy polyester mesh at a screen printing supplier (look in the yellow pages), or you can try out various kinds of very fine weave polyester mesh from the fabric store, or order from online.
Check out some of these links for lots of info on screen printing: