a few questions about the HP photosmart 2575 printer

Hi, i was looking at this printer as a replacement to my Epson dx4850 printer.
i was looking at the spec and found out i could plug it in to my router and then anyone who uses the internet via the router aka my family can print from it.

but how does this work?

If you get it all working and then plug it in to the router how do you print from it?

do you go file,print and click on find printer and it will find it or what?

i dont quite get how you are meant to find the printer if its attached to my bt voyager 2091 router and print to it?

Also that way i couldn't check ink levels but oh well.
that would mean one less usb port used and less stuff to run on my pc.

thanks in advance
lodore