It appears that you may be confused about how a router (like the AirPort Express or other router) functions.
Devices on your "local" or LAN....either wired or wireless.....can communicate with other devices on the same LAN......and the Internet is not involved at all in the data transfer.
For example, you have two Macs connected to the AirPort Express and you want to transfer or copy data from one Mac over to the other Mac........either over a wired Ethernet connection or via wireless. The data transfer occurs only over the LAN.......it does not ever reach the Internet.
So, although both Macs might be able to connect to the Internet, if you are sending data between the two Macs, the data transfer occurs only over the LAN. It does not ever reach the WAN on the AirPort Express.
I understand there may be a way to keep traffic among local devices LAN? from needing to go over the Internet WAN?
How can I set things up to do this?
You do not need to do anything. Things will occur automatically, so there is nothing that you need to do to "set things up". In other words, there are no settings on a router to do what you ask......since the router is already taking care of this automatically.