“Notarize this” can mean several different things. Each act has its own procedure and certificate. I can explain the differences, but the document, its preparer, the receiving organization, or your attorney must tell you which one is needed.
Acknowledgment
You appear before the notary, are identified, and acknowledge that you signed the document for its stated purpose and in the capacity shown. The signature may have been made earlier.
Jurat
You appear before the notary, take an oath or affirmation that the statement is true, and sign as the certificate requires. Do not sign early when the jurat calls for signing in the notary’s presence.
Oath or affirmation
Both are solemn promises to tell the truth. An oath may use religious language; an affirmation is a nonreligious alternative with the same purpose.
Read about oaths and affirmations
Proof by a subscribing witness
In limited situations, a subscribing witness may appear and swear to facts about another person’s execution of a document. This procedure has specific identity and eligibility requirements and is not a routine substitute for the signer’s appearance.
A notarial act addresses identity and a particular procedure. It does not prove that a document is true, lawful, enforceable, or suitable for your purpose.