How do I know if I have a good Pilates instructor?
Do you have any formal training?
How many hours did you study before you received your certification?
Do you have liability insurance?
Are you a part of any associations such as the PMA (Pilates Method Alliance)?
What is your training in human anatomy?
Do you or have you ever had a mentor?
These questions are a good place to start. It is great if your instructor has completed formal training, but not all programs are created equal. Some are short and include only mat work. Others require the teacher to have taught many hours before they are released into the wild to get paid for their trade.
You want an instructor that understands movement. Knowing human anatomy is very helpful here. You also want someone who has taken the time to understand what each exercise has to offer, how it teaches the body to move differently, and how they can build on one another. Basically one exercise helps prepare you for another, deepening your practice and helping you to a healthier more effective movement pattern. This is why having a mentor or having had one at some point is helpful. A more experienced instructor can help a new instructor understand the method more deeply.
I hope this helps. Happy hunting for a great instructor, there are a lot of quality ones out there.