On my other gardening blog I wrote a post explaining how I repot a cactus to give new indoor gardeners an idea on how to do it without getting pricked by the spines. If you haven't seen that post click the link above and read that entry and look at the photo of the cacti that I'm repotting. Follow the instructions on that entry because everything is the same.
The only difference in that repotting example is that I used a strap I fashioned out of newspaper to keep the spines of the cacti from stabbing my hand. The photo above shows how you can use a chunk of Styrofoam to protect your hands from the cactus spines by pressing the spines into the chunk of Styrofoam. If the cacti soil is dry you can easily lift your plant by gently pulling the Styrofoam up and setting your plant into the new pot.
If the cactus doesn't easily lift out of the pot you can place your palm over the barrier and tip your cacti over and slide the pot off. If your cactus is too large or a columnar shape take two pieces and create a "sandwich, " by placing the plant in between the two barriers and lifting the plant out of the pot.
Always make sure that the pieces you use are thick enough so that the spines don't pierce through and go into your skin. When you repot your cactus I suggest you use a terracotta pot and that you only go one size larger when choosing a pot. If you use a pot that is too large you'll have trouble keeping the soil of your plant evenly watered and eventually your plant will suffer.