Here are some places I would start - Recommendations from a friend or neighbor, the local Senior services or Council on Aging.
Make sure the person you interview is the one who will come to your home, that they have their own liability and worker comp insurance, and ask to see a current background check. The woman my daughter has used for 3 years checks and insures all of her employees this way, and once every 2-3 months does my daughter's home herself to be sure her workers are cleaning as they should be.