I've seen finished pictures like this before, but never quite knew how it was done. But a special birthday present was needed and so I thought it was time to give it a go.
I bought a permanent marker with a 1mm tip for the drawing, although Miss 3 pressed so hard with it, I could have chosen one with an even finer tip. I used some good quality heavy paper, cut it to size, and drew the border on. Then I gave the kids instructions to draw inside the border, and then to paint every bit of white inside the border.
For the paint I used watered down water colours. I could have perhaps made them less watery and achieved brighter colours. It was important to teach the kids to wipe the excess water out of the brush. I did want the colours to run together a little, but not with whole puddles on the paper.
I asked Miss 3 to draw her picture in lead pencil first (to make sure it was an interesting picture from an adult's perspective, not just a big scribble), and I had planned on drawing over her lines with the pen myself. Of course, being a very independent crafter, she ended up doing the pen herself. So in retrospect it probably would have been better to skip the pencil step.