Lay your cardboard flat on the floor, then lay your frame on top of it. Trace the outline of the frame onto your cardboard with a marker.
Cut out the square shape you drew using a box cutter. Cut along the inside of the square so that your piece of cardboard fits snugly inside the frame.
Iron your shirt to remove any wrinkles and lay it face down on your work surface.
Place your cardboard square on the middle of the back of the shirt. Fold the shirt back over the cardboard square, pulling it tightly. Tape the excess fabric to the square and to itself to hold it in place.
Flip the square over and make sure that the design is centered the way you want it. If not, flip it back over, remove the tape and try again.
Press your shirt, attached to the cardboard, into the frame. Replace the frame's backing and display your newly-framed shirt.