Being the recipient of a power of attorney comes with various duties, including signing documents on behalf of the person who gave you the authority, the principal. You, as the agent, or attorney-in-fact, must sign documents for the principal in a way that clearly shows you're signing in place of her because you have the power of attorney. Signature rules vary by state and even by institutions within the same state, but there are some general methods for signing as an agent.
Contact a representative involved in the papers you're signing. For example, if you need to sign a check, contact a bank officer. If you're signing for a real estate transaction, contact one of the attorneys involved. Ask what method of signing is preferred.
Sign the documents as you are instructed. If you don't have a representative to ask, check state laws regarding power of attorney signatures.
Use standard wording if you're unable to confirm how you should sign. A common format is signing the principal's name and writing, "By (your name), as (agent or attorney-in-fact)." Another option is signing your name and writing, "As (agent or attorney-in-fact) for (principal's name)."