For my first trip back in November I had the characters sign a T-shirt. It's true that the characters won't sign your shirt if you wear it that very moment.
So make sure you have something sturdy with you to put under the shirt so it's easy for the character to write on. I used one of those grey standard WDW photo & autograph books, they're stable enough to give support and are just the right size.
Decide BEFORE walking up to the character where exactly on the shirt you want to have the autograph, put the book (or whatever you might use as support) underneath, make sure the shirt lies as flat as possible on the support, take the cap off your pen and you're good to go.
Make sure you use a thick pen, one of those waterproof black sharpies work best. And say THANK YOU to the characters and CMs involved.
I received a lot of comments from other guests waiting around me, as well as CMs, they all thought it's a very fun thing to do, something different than the standard autograph books. Not to mention the characters were excited and had fun signing it. I found the character attendants very friendly and helpful, they often assisted and held the shirt while the character was signing.
Here's a good pic the Photopass guy did of Mickey signing my shirt:
Thats how my shirt looked like after a week at WDW:
Have fun collecting the autographs.