[Coda]

If it helps you feel any better, this kind of field diagram is are ALL ABOUT intuition. They're useless for specific analysis of field phenomena; they exist purely to give you a qualitative idea of what you're looking at. The process of drawing one is a way to translate your mental processes into something easier to visualize.

You use a vector field plot -- that is, the grid of arrows we were looking at a couple pages ago -- or a contour plot (curves of equal field strength instead of curves describing the path of a particle) if you need something more rigorous.

That strategy sounds pretty reasonable. Personally I would start off marking evenly-spaced points around each charge so that I have an idea of what the line density is going to look like before I start drawing and what direction they're going to start off in, and then I'd connect the dots where there's an obvious interaction between the charges, and finally I'd fill in the paths that diverge away from the charges since then I'd have an idea of where the lines need to be spaced for those.

(In reality, me being Coda, I'd hack up a quick rendering program that would throw out some test points and trace their paths on the screen.)

EDIT: Actually that sounds fun. Maybe I WILL do that.