Make a mixture of half sand and half peat. Fill the thick pot to within 6 inches of the top. You need a very thick pot, since Cylindrica grows thick rhizomes that will break thinner materials.
Remove your Cylindrica plant from the pot and check the rhizomes and roots for rotten spots. It is common to over water succulents and they can mold and die if the rot is allowed to spread. Cut out any soft rhizomes or black roots before you pot it up.
Place the plant in the pot and fill with more sand and peat mixture. Press down and water the plant until the moisture leaks out of the drainage holes. Put a 1/4-inch layer of gravel on top of the soil as a mulch and to conserve water.
Set the plant in a sunny location where temperatures are at least 60 degrees F for optimum growth. Cylindrica can grow a foot or two per year. They will do fine without fertilizing but if the plant loses vigor or the leaves fade, give it a small amount of cactus fertilizer diluted to half strength. Follow the package instructions for the proper amount. Fertilize once or twice per year, but never near the dormant winter period.
Water the plant once a month in summer. If there is shriveling in the leaves you can water again, but water sparingly. Water just until the bottom starts to get damp. Allow the Cylindrica to dry out completely between watering. Over watering is one of the biggest killers of the succulent, causing the leaves to loosen and fall out.
Propagate the Cylindrica plant by cutting a leaf and putting it in peat or a sand/peat mixture. The plant will eventually grow a rhizome and put out roots. They take months to root, but there isn't anything to the process.