Try and make a call out; if that works, then contact Sprint directly, as there must be some sort of issue on their end about not having your number configured correctly.
If you can't call out or get calls, check to make sure you have signal (duh). Next, turn off your phone and make sure that your SIM card is inserted correctly by removing the cover to the battery compartment of your phone and looking for a card that looks like this:
If you can't find one of these in the phone, check your original packaging for such a card; it must be inserted correctly in order for the phone to do anything. (This card essentially tells the phone what phone number it needs to listen to and on what network; without it, it has no idea what to do.) If you can't find a card, contact Sprint and they will send you a new one for free/cheap.
If both of those fail, either (a) you have a defective phone, or (b) Sprint hasn't activated your phone. In either case, you'll need to contact someone from Sprint about the problem. I suggest going to your local Sprint store and asking them for help; usually you can get things done a lot faster in person. If you can't do that, try contacting Sprint directly.
Contact info for Sprint:
888-211-4727
http://www.sprint.com/contactus/
Good luck!