Spray degreaser on the silkscreen and then wipe off and allow it to dry for a few hours. Coat the silkscreen with a light, sensitive emulsion solution available at most art and craft supply stores and allow it to dry overnight.
Place your paper logo underneath the silkscreen (flat side down) and set the silkscreen under an ultraviolet light source. Allow the silkscreen to be exposed to the light overnight.
Spray the silkscreen with a pressure washer. This will wash away emulsion areas covered by the stenciled logo; the uncovered area will be hardened.
Stretch the T-shirt over a flat surface. Place the silkscreen on the T-shirt (flat side down) and pour a tablespoon of your chosen acrylic ink color inside the silkscreen just above where you will place the logo.
Drag the rubber printing squeegee from top to bottom, i.e., drag the squeegee toward you. This will pull the ink over the exposed shirt. Do not drag the squeegee back away from you. Reposition the squeegee at the top and drag it toward you again to add a second coat.
Dry the ink using a hair drier for about 20 minutes or leave it set in for 24 hours.