Accessing and hacking a school network.
 

First, my school has a network allowing students and teachers to log in on any computer. Due to lax security, I managed to get access to an admin account on a single computer. How would I proceed from here to get access to the network and ultimately establish an admin account there?

Also, does anyone know if/how it would be possible to get access to the network from home? I don't know what specific program they are using for the network, bu I do know that they are using Vision 6 for remote viewing and control.