MATERIALS:

1 Screen (see note)
1 Kit containing photo emulsion and activator
1 Squeegee
1 Printing inks (see note)
1 Duct tape (a.k.a. "Duck" tape)
1 Whatever you want to screen on to

PHASE 1: PREPARING THE SCREEN

Mix up the photo emulsion according to directions on the box. Keep in a cold, dark place (i.e. the fridge). Usually, the emulsion stays good for about a month or two depending on brand, but in my experience, it has a quality curve. During about the first week or two, it's too goopy on the screen and washes out easily. Also, within the final weeks of its life, it gets harder and is more and more difficult to wash out. Try it out and find your best experience.
Wash the screen in water with a little mild soap. This washes out any manufacturing residues and helps with emulsion adhesion. Set in a breezy spot to dry.
Select the design you want to screen and photocopy it onto a transparency. This can be done at your local Kinko's, etc. Make sure the design looks okay and keep in mind that although silkscreening is a fairly precise art, it is impossible to achieve perfect resolution in your own home. Again, play around with it.
When the screen is dry, apply the emulsion to it using the squeegee. START WITH A SMALL AMOUNT! As with anything, a little goes a long way. Make sure to spread it on both sides of the screen and get it into every corner. Watch out about using too much, if you use too much it will drip all over the place and get very nasty. Once you get a nice coating, set it in a cool, DARK place to dry (i.e. the cupboard). Make sure it stays out of the light as the emulsion is light-sensitive.
Get yourself a large piece of black paper and set up several bright lights above it.
When the screen is dry, place it on the black paper (the paper should be big enough so it covers the surface underneath the screen and absorbs any stray light) with the "bottom" side up. Use tape to secure the transparency (making sure it is backward) to the screen in the area you want to use. Any part of the screen that is not exposed to light (areas covered by the black on the transparency, taped areas) will wash out. Try to keep the tape to the boarders. Tip: Instead of tape, use a large piece of glass or plexiglass to press the transparency to the screen. MAKE SURE THE GLASS IS CLEAN!
Expose the screen under the bright lights for approx. 30 min. Follow the instructions on the emulsion.
When the time is up, wash the screen under a steady stream of lukewarm water. The stream will wash out where the transparency blocked out the light. It does take a little time for it to wash out, so be patient when washing. Lightly rubbing the areas you want to wash out will speed up the process, but be careful as you may rub out an area that you want to keep.
When the screen is washed out, set it aside to dry. The emulsion should've formed a plasticy coating on the fabric.
When the screen is dry, take the duct tape and tape all around the outside edge where the screen meets the wood. This will prevent any ink from seeping under and coming out when you don't want it to. Also, tape anywhere else where there isn't a design as this will strengthen the screen and make it last longer. When this is done, you are ready to print!
PHASE 2: PRINTING

Before producing a final product, the screen must go through several test prints to check for leaks, etc. This is done on paper. Try to use a heavier paper as it absorbs the ink better.

Place the screen on the test paper, making sure to protect the surface you are doing this on.
Take a spoon or similar utensil and place a fair amount of ink across the top edge of the screen. The ink should be anywhere from thick but flowing to peanut butter consistency
Take the squeegee and use it to drag the ink across the screen. You should do this once the first time and then, depending on the thickness of the ink application, you can repeat back and forth as many times as you need.
Check the printed product: Is there ink where you don't want it? Tape those areas (after washing the screen). Is there too little ink on the paper? Do more passes with the squeegee. Once you are satisfied with the product, get ready to test it on the final items you want to screen.
FOR A POSTER: Simply repeat the test procedure on the poster paper.
FOR A TEE SHIRT, ETC: Wash the shirt first. Place a thick piece of cardboard inside the shirt under where you want to screen so the ink does not seep through. Make sure the shirt is flat and perform the procedure used to make the test print.