Simple. The person receiving the Gift signs a receipt that basically says: "Received from X such-and-such amount on such and such date. Signed, Y". Simple.
It might be useful to know what is your purpose for wanting to record the transaction. If it is for some kind of tax issue, the receipt should be signed by the recipient which will verify receipt of the money. The recipient of money is always the one signing any receipt. Include the date, the amount and any other information you want, but get the recipient to sign it.
It should probably include the name of the parties, the date, the amount, the fact that the transaction is a gift transaction and not a loan, and the signature of both parties. You can have "duplicate originals" so each party can have a signed copy.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.