T-shirts work well, too. I looked at several sets of directions listed on Recycled Into Yarn, and then tried this technique:
Step 1: Cut off the bottom of the t-shirt, below the underarms. Cut off the hem too.
2. Fold the tube of fabric from one side to the other, overlapping except for about one inch.
3. Starting at the bottom, cut strips about 1/4" wide up from the bottom, stopping about 1/4" from the top.
4. You'll end up with something like this. Now, this is the tricky part: Starting on the left, cut the very first loop up near the top. Then, cut the next loop diagonally from right to left--you'll always move from right to left. (e.g. from loop 3 to loop 2, loop 4 to loop 3, and so on).
5. Wind into a ball, stretching the "yarn" as you go so that it rolls in on itself. (This worked for the t-shirt, but not the flannel pillowcase I also attempted.) Voila! T-shirt yarn!
We'll documents our strategies for sheets on Monday. This should be more of a challenge, because frankly my wrists got sore after cutting up three t-shirts. I'm thinking ripping is the way to go!