Typically I'd expect an ethernet network, with computers connecting via patch panels to a dedicated server room. Client-side, I'd expect the computers to all be part of a domain, with globally-significant usernames/passwords. From the server room I'd expect a series of switches interconnecting and leading to a central router of some kind that carries the main feed out of the school. For VLAN segmentation, I'd expect a simple "router on a stick" topology, possibly segmenting based on invididual classrooms.The main gateway would likely connect to a local education network within the school's municipal region via VPN across the public network of their Internet provider.
Internet speeds and WAN technologies can vary widely depending on the size of the schools. Could be anything from dedicated point-to-point fiber, aDSL, cable modem(s), full or partial T1's, T3's, frame-relay circuits, etc.
All in all though, your question is pretty broad. Even the term "network" can be ambiguous, since I'm not sure if you're interested in the LAN topology or how you'd set up a domain controller and roll out a consistent software platform for the hosts.
Hope that helps...