Screenprinting from a hand-cut stencil is easy. Just get some screenprinting paper (it's smooth on one side, rough on the other), cut out your design, put the paper on a screen with the smooth side towards the screen and print with a squeegee. A screen is made like a frame except you don't have to mitre the corners, just but them, then staple on a screen (traditionally silk but now polyester), tape around the edges. A squeegee is a long (same width as your inner screen) piece of wood with rubber running along the edge. Buy screenprinting ink (for textiles). Place the screen over the fabric, put the ink on top of the screen and pull the ink down with the squeegee. You should get about 20 or so prints out of this. It sounds complicated but is really easy. If you're near an art school where they do printmaking, you can drop in and they'll show you. Art schools are usually pretty friendly. Good luck.
If there is a shop near where you live that make prints on T-shirts using the silk-screen or iron-on process, then you could call them and ask them to help you. You can bring your own design for them to put on a t-shirt that you will buy at their shop.
Another far less expensive way is using the iron-on pages of T-shirt transfers (they work only on white t-shirts). You take a page, print the design on it with your inkjet printer and then you can iron the design on a t-shirt. You can find these and more info on their website www.myPrintWorks.com