Finding a good GMAT teacher is largely a matter of trial and error. There are a few things to look for, and some things to watch out for. For example, you should insist that your teacher have an official GMAT score, and one at least 20% higher than your target score, or what could they teach you?
OFFICIAL SCORE REPORT
The primary requirements of a GMAT teacher are skill in teaching and skill in test-taking. As a certificate of the skill in test-taking, there is no substitute for an official GMAT score. There are many, many English teachers who will not manage to beat all three questions types on the Verbal section, and equally you may be sure that an MSc in Math or Economics is any guarantee of beating the quant section. The main problem these subject matter experts have is the timing. They have not cultivated the skills to perform under time pressure. Insist on proof.
EXPERIENCE IN TEACHING
Skill in teaching is equally important, but unfortunately less easy to spot. Teaching, like waitering, is a profession: anyone can enter, but few will survive. Those few typically do the job so well that it looks easy. Long-time teachers can tell effective teaching at a glance, but new students often mistake confidence for skill, and could end up like the proverbial lemming, running right off the edge of a cliff. Find reviews, if possible, and avoid big commitments, in any case.
It is wise to meet with more than one potential tutor. Often, the pressure is there to find one teacher and then commit. Why is that? Most great teachers are in it for the long-haul. Most of them know you'll come back for a great service, and therefore they feel little pressure to sign you on a big package deal. Visit more than one, and you'll maximise the chance of finding the best one for you.