When you're wearing a bra, they measure the fullest part of your breasts to determine the cup size, and the band (about the ribs). Then they'll give you an assortment of different bras to try on and judge the size based on each one they give you. Some bras fit differently, so your size might fluctuate depending on which style you want to wear.
A bra fitting is where they take the measurement around the fullest part of your breast to determine you cup size (a, b, c, d, etc) and then they measure your rib cage where the band of the bra wraps around you for the size (32,34,36,38, etc). You can leave you top on, some may suggest to see what kind of bra you are wearing or how it fits now and measure you with just your bra on if you've never been fitted before. But if you are uncomfortable with that they let you leave your top on.