How do I keep my child's molluscum from spreading?

Keep the skin moist. The easiest way to spread molluscum is by scratching at dry skin- this typically unroofs the virus and then the child "auto-inoculates" another place on the skin. I generally recommend keeping the skin moist by using a good moisturizing lotion/cream at least twice a day. If the spots are becoming unsightly, call your doctor about possibly having them treated though they often go away on their own.
Have it treated. It's not called "molluscum contagiosum" for nothing - those pesky bumps tend to spread locally on the body, and then to other kids' bodies. Stop it from spreading by having it treated. Dermatologists use a vesiculant called cantharidin, or freeze them with liquid nitrogen. Imiquimod cream is often effective as well, although that is an off-label use of that medication.
Cover or ignore it. Molluscum occasionally become itchy & scratching the area can spread it . A simple bandaid or other cover can help prevent the spread if it is localized. If the area is broad, just ignore it as the body will eventually shed them all within a few months. If a few become inflamed as they begin to shed, treat as if a simple cut or scratch to prevent skin bacteria from causing a localized infection.
See a dermatologist. for treatment. They may go away on their own, but will probably spread on your child and possibly to others first.