One of my many, early jobs in the industry was as the guy who silk screened those large, sale price signs that are taped to a grocery store window each week.
It begins by cutting a stencil out of a large sheet of cheap, but sturdy paper, such as butcher paper. This is available in large rolls at many art supply stores. I started with a large, soft bristle paintbrush to draw the figures and characters. Being an experienced sign painter really helped me do these quickly in freehand. Then, with an exacto knife, I cut out the letters and numbers from the paper. Some of the tricks involved how to leave in strips of connecting paper strips to hold the "voids" or hollow areas to the stencil, such as the middle of an "O" or zero, or the center part of an "A", "P," or similar character.
With a clean screen, ready to go, I lay the stencil, face up on a stack of paper to be printed, then lay the screen over it. I added a puddle of ink to one end of the screen and then passed the squeegee lightly across the screen. The wet ink would "wet" the stencil, causing it to stick to the screen. Each print would require one "wetting" or flood stroke and a slightly firmer, return stroke to press the ink through the screen onto the paper being printed.
Lift the screen and the stencil came with it. Remove the printed sheet and lower the screen onto the next. Just repeat the process for each print. When I printed the required number of each sign, I peeled off the stencil and tossed it out. The paper stencils were used only one time for a small number of prints. In my case, usually less than a dozen of each.
I used water based inks, so I simply rinsed off the ink, daubbed the screen dry with a shop towel and then place the next stencil down and started over.
It is the easiest screen printing method there is. It is possible to create some fairly elaborate and beautifil screen prints using paper stencils. I played around with the lallrge silk screen set up at my job by coming in on weekends.
Are you going to be creating the t-shirts yourself or having someone else do them?
Silkscreen is a printing process. Acrylic is a paint. You can silkscreen with acrylic paint, so I'm not sure how you are using these terms.
Let's assume you are going to create the shirts yourself. Visit your local hobby store and purchase fabric ink, a breyer (this looks a little like a miniature rolling pin on a handle) and a squeegee small enough to fit inside your silkscreen.
If you want to make a few shirts with the same design, you can mount a piece of organdy on a frame. The frame can be the full size of the shirt and framed from wood or just a portion of it. One Girl Scout troup I led did this project with organdy stretched over large embroidery hoops.
Create a stencil. For a large, coarse image, cut your design from a brown paper shopping bag. You can secure it to the organdy with mucilage glue. For a more intricate design, paint it on the organdy with something that won't disolve in your ink -- such as acrylic paint. (Just remember, if you paint it, the organdy cannot be reused.) Be sure to leave large enough open spaces for the ink to pass through the organdy onto your shirt. Your stencil will block the "white" areas of the design. Any open spaces will allow ink to pass. If you aren't familiar with how stencils look, visit a hobby store and look at the stencils they sell.
If you want to do two color printing, you will need to have two equal sized screens and gauge your stencils so they over lap in the blocked areas and are open where you want that color to print. But that's more of the silkscreen process than I want to explain here. Entire books are written about silkscreening.
After you have your stencil secured to the organdy, you will need to print. My Scout troup worked outdoors. If you are inside, you may want to protect the table and floor with old newspapers. Stretch the t-shirt flat on the table and secure the screen over it. Put your fabric ink in a shallow pan and roll the breyer in it to cover the breyer. Roll ink over the inside of the silkscreen to cover the entire design. Smooth it out with the squeegee, moving all the excess ink to a solid part of the screen where it won't leak through to the shirt. Lift the screen carefully and move the shirt (still flat) to another area to dry. Go to next shirt.
Clean the screen, breyer and squeegee well when you are finished so the ink doesn't dry in your image.