It’s unusual not to want to share even one file.
I’m assuming it’s a proper wireless printer with a built-in 802.11 card. The software will differ from each manufacturer, but it is similar to this. Before starting the initial installation, make sure you have a USB cable to hand and that you know your Network Name (SSID) and Security Key. Install the software and follow the screen prompts to set up the wireless connection for the first time. Once it has been set up you can remove the USB cable from that computer.
On second and subsequent computers, install the software and follow the screen prompts for an additional computer (or similar wording). After entering the SSID and Security Key, the printer should be recognised.