Pick a trainer you enjoy. Avoid trainers who promise you unrealistic results or who push you to buy products such as nutritional supplements or heart rate monitors, especially if they are getting a piece of the action. Some personal trainers will offer a free, initial workout to potential clients. If you can, observe the trainer as he works with another client. Make sure he's paying full attention to that client, rather than talking to other people, checking out everyone else at the gym, and so forth.
Accidents can happen within seconds.
And that session is paid for by, and should be dedicated to, the client.