Cactus should be repotted when their roots show through the holes of the pots, typically every two to four years. The best time is when they start actively growing in spring, often in January or February.
Thick leather gloves are a good idea but may not protect you from stout spines. A smart trick is to use a pair of barbecue tongs to gently lift the plant out of its old pot.
Loosen the roots and inspect them for signs of rot or disease before putting the cactus in its new, slightly larger pot. Fill in around the root ball with a coarse, well-drained potting mix, and be sure to keep the plant at its original depth.
Wait a few days before you water the first time, and then your repotting work is done.