2nd computer needs a wireless network card. It's an easy thing you can install yourself with a screwdriver by looking at the instructions it'll come with. It's basically a little PCI slot card that will have an antenna stick out the back where all your cords plug into.
I'm a blond, I've done it, you can too.
The old version of wireless data transmission was called Wireless B. Wireless G came out a few years ago, leaps and bounds faster and stronger in signal than B. Now, wireless N has come out. I haven't tried it yet so I don't know how good it is. I believe it's all backwards compatible.
I personally like Linksys as a brand, but they irritate me because they outsourced their customer service to India. But the are relatively easy to configure, and this is very nice.
Most routers are made for cable, so finding a DSL one is a little more difficult.
I'm trying to visit linksys.com right now, and I just get a blank page. I'm shopping for one for my Dad right now, and I want to compare models. I'll post any further info I find out.
Basically, you get what you pay for in a router. Belkins fail on a regular basis and are most useful as doorstops.