Ask HN: How best to introduce young children to computing?

I have a four-year-old child who I'd like to gradually introduce to computing. I don't have ambitious dreams of creating a coding prodigy; I do remember a (late) childhood of games and tinkering and would like them to be able to explore the possibilities.

How have my fellow HN readers attempted this? Games first? Edutainment <shudder>? Start with an emulated Apple II and advance the state of the art at twice real-time from 1977? I'm at a loss. Your expertise or war stories would be appreciated.