Aside from the actual baby news, the way that your due date is calculated is one of the biggest surprises for many moms-to-be. When you book your first prenatal visit, they'll ask how far along you think you are, so you'll need to at least try to do the math.
Instead of calculating from the day that you think your baby was conceived, you'll want to count from the first day of your last menstrual period. If you've been trying to get pregnant for awhile and have been tracking this info, this will be easy to do. If it's a complete surprise, make your best educated guess, and don't be alarmed if your doctor informs you that you're actually off by a week or more at your first prenatal appointment.