Step 1: Starting off
First you should get hold of some extremely fine plastic line. Fishing line would probably work, as long as you can find one thin enough. I'm using a plastic line that's meant for sewing beads and such to clothes, it's about as fine as the hair on my scalp. This would probably also work with regular fabric thread, the key is to have it as fine as you possibly can get hold of. Even though thicker thread is stronger we're going to use it in a way that makes the thinner thread both strong and durable.
Second thing you're going to need superglue, the faster it dries the better. It's also easier if you can find a superglue with a brush already in the bottle as it will facilitate steps further down the road.
Third, and final, an X-Acto knife for all your cutting needs. Though, a scalpel or a really sharp knife, or even scissors, would work too.