One way or another, your computer needs to communicate with your printer via your home network.
Both devices should be connected to your home router. It doesn't matter if it's via Wired or Wireless; you can mix and match - as long as the router sees both your computer and the printer, you will be able to print. As such, you don't need a USB WiFi adapter for your computer, since it's already connected to your router via Wired.
The only thing you have to do is connect your printer to your router. The best way to do this is via Wired, as there is no configuration to do, you plug it in, and it works. You can also connect it via wireless, in which case, you have to somehow enter your WPA Key for your router's wireless network onto the printer by fumbling with the little menu buttons. This method could very well work for you, but I consider it inconvenient and unnecessary to have a "Wireless" connection to my printer - I just install it near the router and connect it by cable.
If your printer includes only WiFi connectivity (no Ethernet port), then you don't have that option. I'd recommend against using this printer, for the same reasons as above; having to possible reconfigure the printer's settings from time to time when WiFi has trouble.
It's probably also possible to make a point-to-point connection to your printer using that USB WiFi card - but that sounds downright awful.
