I have 2 ADSL connections with the one ISP serving 20 students for their laptops and smart phones. Someone suggested I set up a "linux box" as a server to monitor and control who is on the net and to exclude my neighbours and student's friends. What does this mean ? Where do I start with such a setup? or where could I find someone who could do it for me if it is difficult.

if they are using a wireless connection just enable encryption and put a password on it.
that will kick off your neighbors. as for friends, you can enable MAC or hardware protection on your router. this uses the MAC address of the connecting device to allow connectivity.

i don't see a reason for a linux router, as these options are usually available in your router that you have or the ISP gave you.

unless there is some functionality you need that i missed?

When that someone told you to "set up a Linux box" did they leave their address for you to ask them? Your ask sounds like you first need to get to grips with what Linux is at all, so setting up a Linux box (=="computer running Linux") as a router may not be as trivial as it could be...

But the gist of it, as I understand you is:

Do you mean you have two wired connections and thus two wireless routers providing wireless to your students? Did you set that up, or did you have an external provider do this for you? If the latter, you probably might want to query them...

If your wireless points support it, you might be able to use MAC address filtering. Every network device has a MAC address (nothing to do with Apple Mac), so anyone who would want to use the network would have to tell you what their wireless MACs are (laptops and phones) and you can add them to the authorization list.

If your wireless point does not allow that then yes, you might want to setup an actual server machine. A basic example: plug the network cables into your machine (remove the wireless points), and set it up as a network router - iptables (firewall) must allow forwarding, you need to do some extra setup on forwarding packets from one network interface to the other (there's an Arch Wiki article on that somewhere, or just google "share internet connection interface forwarding" for example). For monitoring software.... look around, I've never looked into it myself. And again, you will need to look for instructions for allowing individual MAC addresses.

Try perhaps ClearOS or Zentyal which are already set up for server activities with nice GUI control panels (don't know if they cater for your specific use case though, but if you're curious...); look into VirtualBox if you've never used it, so you can investigate distros without damaging anything. I'll plug my own blog here if you're really not getting this whole Linux thing.

Beyond that, you'll need to do a bit of searching and reading to find the rest out - there are blogs, wikis and manuals galore, and you'll need to level up your google-fu. Linux mantra: Linux is for Learners.