I like to paint the insides and ends of the crossmembers, and the insides of the frame rails, first. I may skip this step if the crossmembers are mostly flat, but if they have an I-beam shape or lots of undercuts, I'll paint them before installation into the frame. Then I'll scrape away any paint where I need to apply glue, assemble the frame, and paint the rest. That's the best way to guarantee you'll "hit" everything and end up with no bare spots- or fewer bare spots. Going with a primer which is close to the intended color helps too, just in case.
Using an airbrush helps put paint into those hard to reach spots, but isn't mandatory. Finding a paint that covers well without overloading the parts is also a big plus. If I just need a basic black frame, I like to use Krylon Rust Tough flat black straight from a rattle can- it covers very well and dries quickly.