There are several things to check out. Walk the list until your problem is resolved -- then skip all following:
- make sure the SIM was inserted correctly (it easily happens to insert it the wrong way round)
- does the same SIM work in other phones?
- yes: SIM should be OK, phone probably "borked"
- no: SIM "borked". Ask your provider for a replacement (Done.)
- do other SIMs which work in other phones work in yours?
- yes: very strange. Check with your provider to send you a replacement SIM: it's rare, but sometimes there can be incompatibilities (especially with older SIMs and newer phones).
- no: pretty sure your phone is broken. Hand it in to service.
Some indicators to watch during the process, as they might prove helpful to service (and for combinations not covered above):
- Do you see a signal in the status bar?
- Are there any SIM errors displayed?
These two are pointing to an answer whether a SIM was detected at all. The phone should display a special symbol in the notification error if no SIM is found, and usually asks the user to insert one.