There are various ways people have used, mainly for spraying, and when painting by hand, you may be better off just doing the top, then the bottom. Hanging it up by the tuner holes in the headstock is one way (though obviously, not when working on the headstock). Some people have used a clamp to grip onto the inside of the neck and bridge pickup routs, and used that like a handle to hold the guitar when painting, then hanging it up on some wire to dry. This is still quite unwieldy, so it's best to leave the neck unglued until you decide its time it all has to fit together. It's often better to paint the front and rear of the guitar when flat, as you are less likely to get any runs in the paint when the surface you're painting is flat, so it does draw the process out a bit longer. But acrylic paint (if you use it) doesn't take too long before it's dry enough to touch and turn over, so you could do a full coat in a day.

Or you hold it by the neck and paint the body, then when that's dry, hold the body and paint the neck. As you are going for a solid colour all over, you don't need to match up a neck finish to a sunburst on the body. so there's less of a need for it to be finished all at once.