More details would help - how will you connect to the server? How many classrooms are there? How many does an arduino control?
That said, I assume the classroom schedule is held on a web server, so you'll need a way to talk to it, e.g. ethernet shield or wifi shield. The Arduino can act as a client and use GET requests to find out what the classroom status should be.
At its simplest, the arduino can pass a hard coded classroom id in the GET request and have the server figure out, based on time of day, whether the AC or lights should be on. Presumably, the AC should come on a little early to be effective.
The lights and A/C will need to be switched using external hardware - relays, or something like the powerswitch tail. The latter is preferable if you don't have experience using mains voltage.
If desired, the arduino can take on more responsibility - pull down the schedule periodically and then do the time calcs for itself to determine what it should turn on/off and when. A RTC might be useful in this scenario. A single arduino might control multiple classrooms too.