For me, the most important aspect is finding someone I can relate to easily. i've been playing so long that I'm not looking for a complete swing makeover, but for fine tweaks and improvements. Therefore, I look for someone who works with the swing you have, not the swing he or she wants you to have. I've been lucky enough over the years to find three of those, and have benefitted from each in different ways.
So, is the pro willing to listen to what you have to say? Are they able to interpret that and make positive, constructive proposals. Are you willing and able to put int he practice tee/range time to engrain those concepts and guidelines into your play?

If you are starting from scratch as far as lessons go, I'd talk to a local retailer. They usually can help you, as they know most of the local pros. Like pulplvr said, let's work on what you are doing well now, and make it better, as opposed to a makeover. A few drills may get you on track faster than you think.....

It is rather easy to find a Golf Professional for golf lessons.
Definitely ask questions and they should ask questions of you as well. I do teaching and I have a conversation with every student to ask about their goals as a golfer, what sports they've played, any injuries whether recent or not, their profession, and list may go on. I need to know the student and have an open dialogue. I send my students home with drills and or homework. Need to keep the student engage and keep things as simple as possible. A goal of a teaching professional should be to help the student self fix while away from the teacher. if they are to self dependent then they can't take it to the course. Also, on course lessons are a great way to ingrain topics on the lesson tee. Good luck and let me know if you have any other questions.