The nail is painting with a base coat, two layers of polish and a top coat as with any regular manicure. The difference is that each layer is "cured" with a UV lamp to secure the color. Unlike a regular manicure, shellac nails are supposed to keep their glossy polished look for up to two weeks without a chip or smudge to the polish. Plus, there is no drying time because of the curing. These are my nails a week after my trip to the spa.
You can also create interesting colors by mixing polishes. Your manicurist will be able to tell you what the color combinations can produce.
Not every salon offers shellac nails, so you will have to do a search to find a salon near you.