I pumped in the hospital to help with an inverted nipple, and then started pumping "for real" at about 4 weeks -- my Dr. said I could start any time after 3 weeks, because the baby was over her birthweight at 1 week and clearly nursing well. The first week was a really pitiful, miserable experience, but it's gotten a lot easier.
I pump twice a day, once in the morning (they say to pump before your first morning feed, but I sleep before my first morning feed; I pump between it and the second) and once to replace the feeding where DH gives a bottle. I freeze whatever I get from the second pumping most of the time. On a good day, I may also freeze some of the first pumping. I pump both breasts almost every time, but a lot of people do just the one they would have fed on if they're replacing the feeding, or feed the baby on one side and pump on the other. (Note that the baby almost never eats from both breasts for me, only when she's in the middle of a growth spurt.)
I have an Avent Isis and a pair of Whisperwear pumps. Both of them have required significant learning periods to get right, and I'm still learning the Whisperwear (a new sort of electric pump). The Isis is actually easy and fast for me now, but it puts more wear and tear on my nipples and it ties me down, so I tend to use the Whisperwear in the morning, so I can do other things, and the Isis at night, when DH has the baby anyway and I'm more interested in speed.