My dependent son received a W2 for an internship that he did through school last semester and I've already filed my taxes! Was I suppose to claim this income (its about $1,000)? Or does he file this on his own?

This income is not reported on your return. If he had any income tax withheld, he may file a return to receive a refund.

The requirement to file is based on filing status, age, and gross income amount. Please see the following TurboTaq FAQ for more information about filing requirements:
https://ttlc.intuit.com/replies/3302274