This is absolutely correct, but maybe too involved and expensive for a (presumably) cheap used bike.. You can get a decent (NOT factory-perfect or factory-durable) finish with spray cans of something like Krylon from Home Depot. Preparation is important, at least 90 percent of the job--every lump and bump and scratch on the frame will show through the paint. Basically:
Take the bike apart as far as you're comfortable with. If you can strip the frame bare, that's best, but if not, just go as far as you want to.
Clean off ALL grease, oil, dirt etc. Scrub with detergent or solvent, rinse, scrub again and wipe with solvent or paint thinner. Every little cranny you miss is a place where paint won't stick.
If you were painting over a factory surface, all you'd need to do now is sand lightly, maybe prime, then paint. Since there's cheap paint involved, you can use a stripper (Jasco is one brand) to remove it, or try to sand it down to a solid, no-flake no-peel no-drip base. Good luck.
Once you have a sound base, evaluate it. I usually prime at this point if there's bare metal showing or if I'm covering a dark color with a light one or if the original paint scheme had a lot of contrast. Cover lightly but completely with at least one coat of primer, let dry, sand lightly (200 grit or finer), repeat if necessary. Then spray on the final coat(s). A few light applications are better than one heavy one.
If you're going to mask to create a design, don't mess with the cheap masking tape from the supermarket. Go to a paint store or big hardware store and get the good stuff. Frog Tape is one type. Let the paint dry for a few days, then wax with any good car wax.
It will look good when you get done, but the paint isn't as hard or scratch resistant as the factory finish. Personally, I don't care--a few scratches on my bike are sort of mementos of where I've been and what I've done--but they drive some people crazy. If you're one of them, the other post has better advice for you, or you could consider powdercoating. If I ever refinish another bike, that's what I'm going to do.