If the person living abroad is U.S. citizen or resident alien, you - as a recipient- are not required to file/declare anything on your income tax return. The gift donor will have to file a Gift Tax Return if the gift was more than $15,000.
If the person is a nonresident alien, it depends on the amount. Per the IRS: "If you are a U.S. person who received foreign gifts of money or other property, you may need to report these gifts on Form 3520, Annual Return to Report Transactions with Foreign Trusts and Receipt of Certain Foreign G...." Per the form's instructions, you must file it if you receive "More than $100,000 from a nonresident alien individual or a foreign estate (including foreign persons related to that nonresident alien individual or foreign estate) that you treated as gifts or bequests." The form 3520 is not included in your tax return. You must download it from the IRS website and file manually.
You can read Gifts From Foreign Person for more details.