You can get a Wireless PCI card, or run a really long ethernet cable

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You can also buy ethernet jacks. Run the cable through the walls, install 2 jacks, run the jack upstairs to the router, plug anything you want into the jack downstairs. That idea may end you up ripping apart your walls though, LOL!
Either way, if you wanted to do a PC-to-PC connection without bridging, then there are 2 types of ethernet cable, and you need to have a crossover cable or they will not communicate. A standard straight ethernet is only used going to a router, or cable/dsl modem. WIth a crossover cable (or crossover adapter ~~ about a foot long) you should be able to communicate, share files, share printers, and play games.