A power of attorney is created by signing a document that is usually prepared by a lawyer. It authorizes the person(s) named to act on your behalf. It does not need their signature. It can only be given by a person who understands the meaning of the document at the time.
The attorney(s) is legally obliged to act on your directions if you are able to give any and they would be guilty of a crime if they just took your money and spent it without your authority (if you were able to understand and give that authority).