Zeroth step - get t-shirts: Go to somewhere with t-shirts. Acquire the right number of the right color of the right size of the right style. These will later be printed on. Remember when picking styles that it takes a small amount of effort to switch ink colors, so unless a lot of people want to help, it is often easiest to stick to about 2 ink colors and pick shirt colors accordingly.
First step - Acquire a design template: The design should be printed onto ordinary paper in solid black, and 8.5 by 11 or less. If you don't have this yet, you and Photoshop/GIMP/gahMSPaintifyoumust should go have a little ... chat with said non-digital or non black and white design. Someone, or some random computer lab on campus can provide a scanner if needed.
Second step - Prepare screen: Go to the LAC at least an hour before it closes. Tell them you want to make some T-shirts. They'll want to know if you've done this before. When you admit your woeful ignorance, they'll get someone to show you how to make the screens. Its really really really easy. Really. In a nutshll, if you can tape, read a clock and follow simple instructions, you've got all the skills you'll need.
Someone from the LAC will check the design for excessive offensiveness. Then you'll be give a plasticy screen thing in exchange for $5. You tape the design on right-way around (I forget, but they'll show you) and run it through a thing that looks like a giant laminator. It melts away the plastic wherever there is ink, leaving only the screen behind. Check at this point that the screen has in fact been melted, even over the very fine lines incorporated into your design. It will, assuming you did get it right way round. Now you tape the screen into a frame, and are ready to print.
Third step - Print T-shirts: Pick a color from the many available to you, pour some into a tray, add a small amount of binder (something like 1:10 binder to paint ratio, and that assuming noone already added binder to the paint you want.) Put the frame into the large wooden many-limbed squid of of screenprinting. Position the poor test t-shirt below this contraption. Lower the frame onto the t-shirt (this is a good time to test if you put the frame in right way around), and use the scraper to push paint through the screen. Yay! Printing! Now do it a bunch more with the real thing.
Notes: If you're printing front and back, you'll need multiple screens, although you can probably get more than one small design onto each screen, and there are small frames to match. Each screen is good for printing on 20 T-shirts, which covers the ink you use as well. If you're printing more, well, pay up. Its dirt cheap, really, and poor form to rip off the LAC.