First, revisit the My Info or Personal Info section to verify your dependent's Social Security number (if wrong, correct it and go through the File section to resubmit your return).
If you already verified this info, you'll need to paper-file your return as the IRS will continue to reject your attempts to e-file.
Then, if you know who claimed your dependent, ask them to amend their return by removing the dependent. Amendment processing can take weeks or even months, which is why it's best to paper-file your return in the meantime.
If the other taxpayer is uncooperative, the IRS will eventually contact both of you to figure out who gets to claim the dependent. The losing party will then be liable for any additional taxes, penalties, and/or interest as a result of the false claim.