Certain items will simplify your trip (Disney World sells most of them in the park if you forget, but prices are high). Disney World involves a lot of walking and standing in line, so make sure your kids have comfortable shoes. For smaller children, bring along a stroller to let them nap when they're tired. Lines can be long, so include a few hand-held games or picture books to keep the children occupied while they wait. Snacks and water are a good idea, too; while Disney World discourages outside food, it won't prevent you from bringing in anything so long as it isn't in a hard-shelled container. Finally, it can get hot in Orlando and it often rains. Make sure your kids have a rain slicker and administer sunscreen before you enter the park.
The Disney company prides itself on maintaining a safe environment, but it helps when parents plan ahead. If you have small children, consider keeping them on a leash or hand tether so they won't wander off. Before moving into the park, find a convenient landmark and tell the children to go to it if they become lost or separated. If they can be trusted with a cell phone or walkie-talkie, give one to them and have them turn it on. (They can also talk to official Disney employees, who wear a white badge with their name on their left chest).
Many of the rides have height requirements, forbidding children from riding if they aren't tall enough. You can either skip those rides or ask the ride operators about "kid switches" if you like, wherein one adult sits with the children while the others go on the ride, then another adult watches the kids while the first adult goes on the ride. It keeps you from splitting your party up while still letting you safely enjoy all of the attractions.
Disney World offers a lot of things to see and do, which can be draining even for the most hyperactive child. Plan for a down time in the middle of the day when you can go back to your hotel to nap, or at least a rest period in some quiet portion of the park. Try to arrange the rides so that no one becomes unduly bored -- mixing rides aimed at smaller children with those catering to older kids -- and pay particular attention to the themes of certain rides. Some -- such as the Haunted Mansion at Magic Kingdom -- may have no height requirement, but contain scary images that may upset smaller children.