Wearing gloves will also help protect your hands as you start placing other succulents around your cactus. I've found it's generally best to start your arrangement by placing the cactus and then working to fit the other succulents in around it.
For larger cacti and those with long spines, I've found that using a towel or newspaper is a great option. Simply wrap the towel around the top of the cactus and use it as a handle to move the plant into place.