Step #1: Figure out how to worth the TV. They will become distracted immediately, at least until the show ends and there’s that five to ten minute wait before the next show starts. Sometimes, they’ll resist. At this point, ask them to go pick up toys in the general vicinity of the TV, wait a minute or two, then go find them staring slack-jawed at the TV. Casually sit down at the couch and wait for them to join you. When the show ends, repeat.
Step #2: Play with them a lot, then get them to take a nap. They’ll be out for at least an hour. The kid I babysat a few weeks ago was out for three hours once. It was fantastic.
Step #3: Get them into fairly self-sufficient activities. For example, playing on the trampoline or with an animal.
Step #4: Guide them towards activities with small mess capabilities. Games with few pieces or a couple dolls are good ideas. STAY AWAY FROM: Monopoly and legos. Unless the kid gets really distracted with the legos for extended periods of time, then legos can be a good idea. The kid I babysat had those big duplo type blocks, but she’d always make ME build stuff, so for my purposes, it was a bad idea.