You claim the dependent on your tax return, and file it by mail. You will not be able to e-file. Ask the other parent to file an amended return to remove the dependent. If they do that, the problem is fixed.
If the other parent does not file an amended return, both of you will get letters from the IRS telling you that the one who is not entitled to claim the dependent should file an amended return. The letters might not come until a year or so from now. If the other parent amends after getting the letter, then it's fixed. If neither of you amends, you will both get a second letter asking for information to justify claiming the dependent. The IRS will then decide which parent is entitled to claim the dependent. The parent who is not entitled to claim the dependent will get billed for the additional tax plus penalties and interest.
This answer has been verified for accuracy by an Intuit expert employee
