We were recently invited to a Kansas State basketball game in Manhattan, KS. Since we live in Jayhawk country, the kids don't own any K-State shirts. I went through my piles of t-shirts that I use for Jill Be Nimble dresses and found one that would work.
I cut out the wildcat and K-State. I used t-shirt scraps I had on hand to cut a slightly bigger rectangle to go behind the K-State cutout. I later cut a square out of gray knit material to go behind the wildcat. I just don't have a picture of it.
Then I used Heat'n Bond to fuse the original t-shirt to the purple rectangle. You can find it at any craft or fabric store. It's sold by the yard or in packages. I typically use Heat'n Bond Lite for these types of projects. It's easy to use, just follow the directions on the package.
Heat'n Bond is a double sided fusible material. You iron it first onto your cut out, then peel away the paper backing. Then you are ready to iron it onto your cut out shape, in this case, my purple rectangle. I then repeated those steps on the back of the purple rectangle and ironed it directly on the shirt.
I ended up sewing around the edges of the appliques, but you don't necessarily need to do that. As an alternative, you could stitch around the rectangle with yarn or use a regular needle and thread and hand stitch around the applique.
Hudson in his shirt at the game.