Gather materials:
You will need to find scissors that will cut through the fabric of your socks. Fabric scissors work best. If you think your socks will fray, if you want to add a deocrative trim to them or spice them up in your own fashion, or if your socks have holes a sewing needle and thread will be needed as well as scrap fabric to make a patch for the holes.

Determine which socks you will be using for arm warmers.

Line a sock up along side your arm to determine where you wish to cut them. Some socks are longer/shorter than so it's always good to judge how they will look on your arms before you bring the scissors into play.

Line up the scissors to the sock where you would like to make the hole to stick your hand through and cut slowly as desired. Slow scissor movements help give the sock the shape you want and keeps your fingers safe too! Look at the toes smile as I decapitate them <3

If your sock has holes in it now's the time to get your scrap fabric and cut out a patch. It's important to make the patch bigger than the hole so you have room to sew and so the sock doesn't bunch up at the sides of the patch.

Once your patch is the size you need place it on top of your hole and sew it to the sock. For a prettier appearance you can turn your sock inside out and line the edges of your patch with the edges of the hole so the seam will not show on the outside of your arm warmer. Or if you're like me and just don't care you can sew it on the outside. I suggest using a whip stitch but other stitches can work too. I used a pin to hold my patch in place while sewing.

Now you are free to hem the raw edge of your arm warmer and add decorations to it as you see fit. I liked mine as is so that's how I wore it. And you're done! I find that wearing them with the elastic band on my arm keeps the arm warmer from sliding down past my wrist.
Enjoy having warm arms while not wasting good socks!