When I visited B's preschool, I looked for how the room was organized and what types of learning manipulatives and toys they had. Was there a section for reading? Pretend play? Was there a schedule for the day? I asked questions regarding safety procedures, preschool's philosophy, what they do if ___ (mine was child cries or if they have to go to the bathroom during recess lol).
In elementary school (I taught 4th and 5th grade) the teacher usually has a lot of info to share with you during those meet the teacher nights. I'd make sure to figure out the way that is best to communicate to him/her (email, handwritten note, phone call) and what materials your child needs to be ready for school. Once school gets started you will get a better idea of things and can make a list of things you want to talk to the teacher about at conferences or by phone/email.
Does that make sense or help at all?