Keep in mind, as the t-shirts are layered, this rug results in a somewhat uneven floor surface and is not well-suited for people that are accident prone or generally have trouble walking.
Step 1: The idea
(I drew this diagram to sell my very skeptical girlfriend on the idea)
Step 2: Collect T-shirts
If you still don't have enough shirts, you may want to see if the regional Goodwill Store has a "last chance" outlet. The shirts found at the Goodwill "last chance" processing depot will be remarkably cheap and are usually moments short of making their way into a dumpster. You may as well put these shirts to use.
And so you ask, "How many shirts will I need?"
My space was 9 x 12. I used roughly 20 - 30 t-shirts.