Fill a bucket with a mixture of 3 parts of all-purpose potting soil, 1 part perlite and 1 part of course sand. Mix the ingredients up well with your hands or a hand spade.
Locate a plant pot that has drainage holes and that is at least 2 inches larger in diameter than the current cactus pot. Fill the pot with 1 to 2 inches of the prepared soil mixture.
Put on gardening gloves and pick up the pot that the cactus is in. Place your hand at the base of the cactus and lift it straight up to remove the entire soil ball from the pot. Set the cactus and attached root ball aside on the work surface.
Insert the old pot inside the new pot and push it down firmly. Pack additional soil mixture into the gap between the two pots leaving 1 inch of space near the upper rim to allow for watering. Water the soil with the old pot still in place to pack it down further.
Remove the old pot from inside the new pot and set it aside. Pick up the cactus and loosen the root ball gently with your fingers. Set the roots into the hole inside the new pot.
Spread a 1/2-inch layer of stones on the top of the soil around the base of the cactus to prevent the soil from splashing up on it.