Choose a cool, overcast day in spring for the transplant, so your agave comes through unharmed. Prepare your new site first by finding a spot that gets full sun and good drainage and mixing in gravel and quick-draining soil to a depth of 12 inches to build the right growing foundation.
Don gloves to protect your hands during the operation. Although agave attenuata is spineless, the leaves may still be somewhat sharp. Use a spade to dig into the soil several inches from the base of the plant to locate the roots. Once you've found the roots, dig under and around them to loosen them from the soil, then pull the plant up. If the baby agave is still attached to the parent, use a knife to sever the attachment, but be careful not to cut any of the roots.
Cut off any of the outer leaves that look unhealthy or damaged, then take your new agave attenuata to its new location. Plant it in a hole as deep and wide as the root ball, then water it with 1/2 inch of water to help it establish. After a couple of days, put the new agave on a standard agave maintenance routine.