First off, odds are it'll be an intro to Training (and sales pitch.) more than a legit hour with the guy. Ya'll'll talk about what your goals are (and it's good to know them beforehand), how often you're able to frequent the gym, how the PT staff is available to help you in terms of either planning or active coaching, and how much the service costs. At least, that's how my "free PT session" was when I joined up a few months ago. I did like 15 minutes of active time with the guy. Even if your goal is to be stronger and be more cardio-adept, don't even mention the cardio in your goal since you can do that later. This'll help the PT focus on the more immediate matter.
There are no ignorant questions at all. I suggest utilizing the time and having the trainer give you an orientation on almost everything they have available and what muscles each machine works, and possibly show you how to do some of the basic compound free weight lifts. There's plenty of literature (I highly, highly recommend Starting Strength) on how to lift, and Youtube university is typically more beneficial than not (cross-reference everything; there's a lot of misinformation, broscience, and bad form instructional vids too), so you might be able to get away without asking about the lifts. But there's no easy manual on many of the machines and while some of them do have pictures basic operation might require an additional step that's good to be edified on. Bring something to write with/on, obviously. Doing this should trump the PT's want/need to actively exercise with you -- there's plenty of time for that later.
The way to get stronger is progressive resistance. If you bench pressed for 30 kg yesterday, bench press 32 kg the next time for the same number of reps/sets. This is also discussed in Starting Strength (and its wiki
). You can go for a lot longer than one month on a program if you're progressing, but it's a handy thing the PT might mention to make you keep needing the PT.