Well, not technically screen printing, but I have dreams of someday doing this the proper way.
With how fast my kids outgrown their clothes I hate the price of all the really fun graphic tees. So we've started to make our own. Old Navy and Target are great for getting tanks and tshirts, often on sale. Michaels has an area of "create your own" whatevers that has some basic colors of fabric paint (don't forget that 40% off coupon you can pull up on your phone). My Silhouette machine comes in perfectly for cutting out designs that we're able to stick right onto our blank canvas.
I know you can do iron on vinyl transfers as well. We have tried those but I don't feel like they hold up to wear and washing very well. Not sure if it was operator error or just not great material that I tried with. I've liked doing our creating this way though since the kiddos can help with the paint.
Wanna give it a try?? Here's what we do.
1 >> wash and dry shirt
2 >> create design and cut out
3 >> apply design to shirt --- this part can be a little tricky depending on the details of the design
4 >> paint! the shirt will absorb a lot, don't worry about using too much or taking a second pass
5 >> let dry for a bit before you remove the vinyl stencil
6 >> wait 24 hours, use a pressing cloth and iron over design to set the paint. Wait 3 days before washing. (per directions on the paint bottle)