How do I tell if my Apple hardware is covered by AppleCare?
Apple's self-solve web portal can tell you whether any Apple product is currently under warranty or covered by an AppleCare plan. It can also tell you when the coverage ends and help you setup an appointment to get your problem looked in to.

You'll need to know the serial number for your Apple product to look up the coverage. There's an Apple support article on how to find this identifier for all the different bits of hardware Apple makes.