Pretty much any trouser or knee-high sock will do. But why not go with one that has a little color!
I wouldn't recommend a wool sock, as it might feel scratchy. And make sure the sock hasn't lost so much of its elasticity that it won't stay on your upper arm while running.
When you cut the sock in half, you're generally looking to have a top half that's about twice the length of your phone.
Take the top half of your sock (which is now your armband), and turn it inside out.
I prefer to put the hemmed side on the top of my arm, but it doesn't matter which way.
Place your phone on your arm and over your armband, so that it's about halfway up the band.
Bring up the bottom of the armband over the phone, so that it holds the phone snuggly. And that's it! You have the best darn DIY armband for running out there!
Now get running!