Get the proper paperwork that is needed to get a power of attorney. This is usually just a piece of paper that should be signed and notarized by a certified notary. You must also be deemed competent at the time of signing in order for a power of attorney to be valid.
Find a notary in your area. One can usually be found at a bank, an insurance company, or a city building. Sometimes they will charge fees, but if you know them, they usually won't.
Take your paperwork into them along with a valid ID. Sign the document and have the notary read it over and notarize it accordingly.
Give your signed and notarized paperwork to the proper individual. This is either a lawyer or the person that is requesting the power of attorney.