I went to my very first coffee cupping on Wednesday this past week at Montana Coffee Traders. To start out they have a table set out with various ground coffees. They're all very lightly roasted in small batches and freshly ground. After a lengthy intro by Richard, the toastmaster (what an awesome job title) about what we were doing you smell them. You're supposed to be smelling it for the overall flavors and the nuances. They even provide you with a list of possible descriptive words including things like "fruity, fermented, baggy, cardboardy, rioy" (which I interpreted to me it smells like a river in Mexico).
After the smelling of the grounds the facilitators, ours was Katie, pour hot water into the cups. Then you smell that. Thirdly you go around and "break the cusp" with a spoon and smell it while you do that.
Lastly, you get to drink it. You take a small amount and slurp it with a spoon (possibly one of my least favorite noises in the world but I got over it for the cupping). While you taste it you're trying to assess the acidity, flavor, aftertaste, sweetness and overall impression. My honest opinion is that I'm terrible at it. I mostly just wanted someone to tell me what I was smelling/tasting. I did however enjoying getting to learn a lot about coffee.