For coffee, one of my old old favorites that's still great is Sant'Eustachio in Piazza de S. Eustachio. It remains popular with locals despite being overrun with tourists. They add sugar by default, so if you want it black, order it "amaro."
For people-watching in the evening, I like Bar Farnese. It's just a block away from the tourist apocalypse of Campo de' Fiori but is much quieter and the passers-by include a higher percentage of locals. If you sit there for any length of time you'll see Bridgettine nuns walking or driving by in their full old-school habits (their motherhouse is just around the corner).
Any decent tourist guide will tell you the basics of cafe etiquette.