separate networks in office

I currently have a network complete with shared printers, etc and 3 PCs which each regularly connecting to a VPN (Db Server) at a remote location - This network MUST remain private (inacessable).

In the same location, I need to provide a separate network for students (and occasional guest) to wirelessly belong to a separate network complete with internet access with their laptops, their I-pads and their I-phones (and whetever else comes on the scene) on a permission granted basis.

I'm told there is no way a computer can connect to 2 different networks w/o overlap of access to the other Network. I know this is incorrect because I setup two separate networks (w/o crossover) in the late 80s by simply using 2 NICS with different IP address in a common server.
Could it be because I was using Novell 3? I think I also did it using Windows For Workgroups 3.11 or maybe it was Windows NT, I forgot.

Just because it's wireless now shouldn't prevent me from building a similar setup.

Surely there must be a way to use separate routers to do the same thing.

Can you tell me what scheme and components are available today to accomplish what I'm trying to do?
Thanks for your assistance.
Scott

 

That's what is essential.
Thanks,
Scott