What will I need?

[Ice9]

I have cox cable and I am building a new computer that will go in my room. What do I need to be able to share the internet from the computer downstairs with the one upstairs... wireless?

 

[Inaris]

Wireless would work, but a wired network is better overall if it's not too hard to install. If you can easily run cable, then do it.
If you can't then get a wireless router and either an internal wirelss card or a USB wireless devise. The rest is pretty easy.