Option one: paint it on (directly, or by making a stencil) with fabric paint.
Option two: get iron-on photo transfer paper, print the design on the paper, and iron the image onto the shirt (caveat: on a bright red shirt, the image might not be as vibrant or stand out as much as you may want it to).
Option three: applique using a contrasting fabric (most complicated and time-consuming method).
Pictures and tutorials from my costuming portfolio at Syagria's Cosplay Site!
Star Trek Original Series Uniform!
Original Creation for AB13
Most Recent Con:
PAX East, Anime Boston 2013