Can I do this wirelessly with Apple and Dell, desktop, laptop, and one printer?

As some of you know, I have ventured into Apple, and now have a laptop. I don’t know anyone personally who has an apple, has a wireless network set up, or even knows very much about computers – and try as I might to read wikihow, google, etc. I still am not sure that I understood this.

I have an Airport. I got the Mac to work wirelessly, the Airport light is green. I set up the wireless printer – but the printer will only work if I attach the USB cable to the airport. Did I not understand this correctly? I thought that by having a wireless printer, that it wouldn’t need to be attached to the computer or the airport. Am I right or wrong?

The reason I ask, is because we are also awaiting a dell desktop that is NOT WIRELESS and does not have a card (all computers crashed and burned, hence the new ones-don’t ask) and I had thought that I could attach the wireless printer to the dell using the USB, and both the dell and the mac could share the one printer.

I also thought that I would use a networking cable to attach the dell to the airport, so that we could get the internet. Have I not understood all of this properly?? Thank you so much for your help.