This project literally takes 5 minutes and I am happy to say requires NO SEWING. By, the way this isn't exactly Grandma's doily. It is one I found in the dollar bins at Michael's.
Place your doily on a piece of ultra strong Heat & Bond.
Flip it over and iron on the paper side, not the waxy side. You might want to put something under your doily or you will have sticky mess on your ironing board.
Peel it off!
Place your doily where you want it on your shirt, and carefully turn it inside out and iron.
That's it! If you feel it isn't sticking you can stitch around it but you shouldn't have any problem. Just wash inside out on gentle cycle.