Decide exactly what you’re looking for. Are you looking for individual lessons, or group work? Do you want classical, modern, dramatic, or comedic training? Do you want to learn musical theater as well? Do you want to do stage or film acting? It also depends on whether you are looking for the acting coach as a hobby or to improve your career. Selecting the right acting coach can not only improve your craft, but give you valuable connections for finding that next job.
Find a website like Backstage or a local equivalent (search your area on Google with “acting coaches” or “acting lessons” after it). Some cities are going to have more choices than others. For example, New York City is going to have more acting coaches than somewhere like Huntsville, Alabama. Yellowpages.com is another good place to look.
Check your local listings in newspapers and art magazines to see who is there. Then make some calls to gather information about prices and specific services offered. Also look under acting schools and vocal coaches; some but not all singers will coach both your acting and your voice, even if they’re not listed under both. Try looking under “Acting Coaches," “Acting Lessons," or “Theater Instruction."
Talk to other actors and your local theater groups. They will know of good coaches for you to check out. Some of these local theater groups will even offer their own classes there, which might be a good place for an amateur to start before you start paying big money for private lessons. These classes can be a lot of fun, a good place to meet knew people and can help you make good connections.