What you mean train in what way? Anyways, I didn't intend to give you much advice on specific routines etc. as I believe your gym trainer should help you exhaustively with that.
Warming up, yes, it's important. Leg day? Hit the cardio machines for at least 5 minutes before. At least. About 5 is usually fine for me though. You wanna do some minutes on the rowing machine if you have one in your gym as well before every training - at least that's what I do.
I suggest you ask your trainer for shoulder warm up exercises as well, if he doesn't give you any. They're very important. If you ever feel pain whilst training your shoulders, stop and ask for advice. I ended up with a small inflammation on both my shoulders; nothing serious, but it's always best to avoid this sort of problems, especially with such a delicate part of your body (shoulders are more exposed to injuries).
Warm up before, but do stretching after too
. It's very useful.
And please don't start taking protein shakes randomly. At least ask for some professional advice before doing that. I personally don't think there's the need to, absolutely not at beginners level, I don't see the point; just eat a lot and make sure your food has nice protein and carb intakes.