To get started, you'll need:
A 6" piece of wire: The wire type doesn't matter. It can be copper, silver, gold or any random base metal that you pick up from a craft store. I recommend the gauge be a little thicker. The wire used in this tutorial is an 18g nickel. The ring in the main image is a 22g sterling silver. The one I wear around all of the time is 22g and I've never had issues with it, but I would not recommend going any thinner than that.
Round nose pliers: The round nose pliers can be replaced with a small dowel rod or a grilling skewer if you don't want to invest in a good pair of pliers, but it will be slightly harder to make the ring. If you do invest in pliers, I would not recommend any pair with quality below the one linked. Your pliers are your best friend in the wire wrapping world.
Flat or needle nose pliers: It's very hard to find a good replacement for these, so I highly recommend these. You can get great pairs of these in plier sets, some of which have lifetime warranties.