Draw or print the design you want onto an acetate sheet. Simple shapes and outlines are often the most effective when screen printing. Remember you will also have to cut this design out.
Use a craft knife to cut out the parts of the image or design that you want to print on the koozie. Place thick cardboard under your piece of acetate while you are cutting to protect the work surface. This cut-out acetate image is your image stencil.
Put cardboard inside the koozie to stop ink from bleeding through when printed. Place the koozie on the work surface. Place the stencil on top of the koozie. Line up the stencil so that the image will print in the desired location.
Lower the silk screen printing frame on top of the stencil. Use masking tape to cover any gaps or areas under the screen that are not covered by the acetate stencil sheet.
Dollop ink on the top of the screen. Hold the screen in place with your left hand. Use your right hand to pull the ink down the screen with the squeegee. Hold the squeegee at a 45-degree angle. This is known as a pass.
Remove the screen from left to right. The stencil will pull away with the screen to show a printed koozie. Leave the koozie to dry.
Pull the stencil off the screen and wash both in water.