Hi, Adair! Welcome to the board!
First – get yourself a book & choose a pattern! There are many (well, at least SEVERAL!) books out there with instructions and patterns, but they boil down to those that use just the T-short logos cut into same-size blocks and those that use them more creatively --cut into different sized pieces.
One new one is TOO COOL T-SHIRT QUILTS – see
http://www.toocooltshirtquilts.com/
Another is THE EXTRAORDINARY T-SHIRT QUILT: A SCRAPBOOK YOU CAN SLEEP UNDER – see
http://www.amazon.com/Extraordinary-T-shirt-Quilt-Scrapbook-Sleep/dp/0978704401/ref=pd_sim_b_3
(You get the idea – just Google T shirt quilts.)
T-shirts are made of knit cotton which is stretchier than regular quilting cotton, so the first thing you have to do is stabilize it with lightweight fusible stabilizer. It's easy to do, but it can take a while. Once you do that, it handles more like regular woven cotton and you can treat it just like you bought it at your favorite quilt store – or went shopping in your mom’s VERY well organized stash. (That’s what she tells US, anyway! -- and if you tell us otherwise, it will be almost as big a scandal as David Letterman's!)
One thing to remember: T-shirt fabric + stabilizer + batting + backing fabric can result in a pretty heavy quilt. Be prepared for that! Some people don’t use any batting at all and just back it with polarfleece. At the very least, use the lightest weight batting you can find.
T-shirt quilts are great fun and preserve lots of memories. Have fun!
BethMI