You don't need the internet at all.
You don't need a modem, as that is something to connect to the internet.
What you want is to set up a LAN. You'll need some form of router or hub to physically connect up all the compters.
Then depending on what OS, you set up a network once all the computers are connected. What OS would you be using? Later versions of windows are much easier to use, and if all computers are using the same version it helps. Most have a wizard style setup, just choose home network.
For the printer, you can either set up a network printer, connected to the router/hub just like the computers, or you can connect the printer to one of the computers and it can share the printer to the other computers. Which is easiest/works best depends on the OS version and the printer.