How often you go to the gym is up to you... you could go every day, you could go much less.
Did the personal trainer show you how to lift weights? How to use the machines? etc etc?
Here is a good website I'd recommend for reading in regards to weight:
In general, you should never work the same muscle group two days in a row. So you can lift weights every day but you'd have to make sure you rotate the muscle groups.