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.
Not every salon offers shellac nails, so you will have to do a search to find a salon near you.