You need to do some research. The best way is word of mouth from other golfers that you know and feel confident about their feedback.
Once you settle on someone plan on an hour for the first lesson–the instructor should interview you about your background, sports played, physical issues, your goals for your game, etc. Be sure to write down and ask all the questions you have. Be sure to make sure that you’ll be able to work on short game and putting as well as full swing.
Never sign up for a package of lessons after the first lesson and if you do sign up for a series down the road don’t ever do more than 5 at a time. Also don’t be afraid that you’ll hurt their feelings if you leave them for another instructor.
Sure signs that you’ve chosen wrongly:
1. Your instructor hits more balls during the lesson than you.
2. Their terminology is too complicated.
3. They say “let’s TRY this” a lot.
4. They don’t have any patience.
5. They don’t use video–it’s a must so you can see things and they have a record of where you were when you started with them. Not having a launch monitor is not as important but most good instructors will.
It’s a shame that I have to mention this but there are a lot of incompetent instructors out there. Find one with a good reputation, who understands how to find the root causes of your problems and can fix them, who communicates well and is patient.
Lastly I can’t imagine taking a lesson and not seeing ball flight. I’m sure there a lot of good instructors who teach indoors and a good instructor doesn’t fix ball flight they fix swing. But being able to see the ball fly is important not only during lessons but also during club fitting.