There's something to be said for starting with something that's already written, and hacking away at it.
That's how I got my start mainly: I'd get some of those old DOS games on a 5.25" floppy... you know the kind, that actually included the BAS source files. I'd browse through it and just start making changes to do something different... to change colors, change text prompts, etc. Before I knew it, I was using the existing game or program as a launching point to piece-meal together an entirely different game. Learning by example like this greatly reduces the intimidation factor when starting out to program. You don't have to know a whole lot to get started, like program entry points, dependencies, etc, you just have to understand some basic logic and flow control (and most 7-year olds will understand "if this, then that"), and you're ready to start hacking at it, learning as you go.
After you've hacked away at it little by little for a while, you'll want to start looking things up and learning how to do more complicated tasks, so a readily-available online reference would also be a big plus.
I'll also add that, like others have mentioned, having immediate feedback is also crucial. That was easy with BASIC where the "IDE" and compiler/interpreter was readily available on all DOS machines. Find something like BASIC where making these little changes is easy and quick feedback is available. Maybe look into some online IDEs?