How do you paint without using painters tape?

Depends on the medium.

Here's how I've done it in the past: Tape the entire surface with what ever tape you're using (painter's tape worked well for me) then use a cutting tool (exacto knife) to cut out your design (might try drawing out the design first, or transfer it onto the tape). Then, proceed to airbrush, spray paint, etc, your design onto your medium.

Caution! My medium was hard metal and the exacto knife did not scratch the surface. Somebody probably could elaborate on a more practical method, but there's an idea. Please note that this is only a single-layer method and if replicated for a second layer you risk the chance of pulling off the paint with additional tape.