When a person has "power of attorney", that person is the agent, or attorney-in-fact, for another (called the "principal") and can act in the principal's capacity. The exact powers of the agent are set forth in the document creating the power of attorney, usually called "Power of Attorney Given to [Agent's Name]". After an agent has power of attorney, the principal should send letters to agencies such as banks and business partners to give those agencies notice that the agent is authorized to act on the principal's behalf.
Address the letter to each agency or use a generic address such as "To whom it may concern" or "Know all men by these presents."
List your name as the principal and list your agent's name as the agent. Discuss when the power of attorney was entered into. Write "On [date] I, [your name], as principal, bestowed upon [agent's name], hereinafter "agent", power of attorney in a document titled [power of attorney document title.] I am writing to give you notice of my agent's authority to act on my behalf."
Describe the specific powers and authority your agent has with regard to the agency receiving your letter. For example, while your agent may have the authority to enter into contracts on your behalf, you may not want your agent to do so with certain business partners (for whatever reason). In your letter addressed to that business partner, explain that the agent has X,Y, and Z in terms of authority to act on your behalf but not the authority to enter into contracts. Tailor each letter to the recipient in terms of what the agent can do.
Explain any procedure your agent must have to identify himself or to act on his authority. For instance, you could require your agent to show both the original power of attorney document and identification.