1 - Location
If you need help with your technique, nothing is going to beat in person training. The number one deciding factor for any gym is location. Typically one that is 30 minutes or less to travel to. This will make sure its easy to get to and thus less chance of not being able to make your sessions for whatever reason.
2 - Knowledge
Has the personal trainer embarked on further education over the basic level of qualification needed? Are they even qualified? The amount of personal trainers out there without the qualifications are astounding. Are they insured? You are trusting someone with your health so it makes sense that you only put trust in those that are qualified.
3 - Experience
Has the personal trainer achieved your goals with other clients? Have they perfected their craft over time? Can you trust them if they have never helped anyone achieve the same goals you are after?
4 - Referrals
Do you know anyone that has trained with them in the past to give you an honest opinion? If not does the trainer have testimonials of real peoples results?
5 - Are they in shape?
Not to put any other trainers down but would you trust someones advice that they cannot adhere to themselves? Its not so much a matter of knowledge as it is principle. We would never ask our clients to do something we wouldn't do ourselves.