I used size 1 double pointed needles. You can use regular needles as well. I like to use double pointed needles with small width projects because it's easy to take along with me.
At first I used mercerized cotton yarn like some websites suggested when making bandages. I felt that for what I needed them, it was still too thick. So I went with crochet thread instead. It was the perfect thickness that I needed. Here's a picture of it.
I cast on at 27 stitches, garter stitch, which made it about 2 1/2 in width, the typical width of rolled up gauze. It was the perfect width for a 3 1/2 year old.
Here is what the final product looks like.
Here's a close up.
Here it is rolled up.
Here's my little munchkin modeling it for me.
First, I spread antibiotic ointment to the boo-boo area. Then I put a little piece of gauze on top. Then I roll the bandage on her and safety pin it. It's pretty stretchable and breathable too.
She loves getting all of the extra attention with her special bandages.