A friend of mine is offering me a free server (not a hosting service but the actual hardware) but I've never run a dedicated server before.

Can someone walk me through exactly what all I would need to get this hardware up and running with my site?

Also, he asked me what specs I wanted for this server. Anyone give me an idea of what I should ask for?

Well, ask for the baddest most monstrous server you think he'll give you, of course!

As for the how, you should start with an OS and go from there.

Linux, Windows, BSD, Solaris, etc and then go on from there.

How to set up the OS for web hosting is a bit beyond what can be posted here.

I'm pretty confident about getting the box setup with some help from this friend, but I am mainly interested in how the heck do I get this box connected to the Internet and get an IP address.

I know this is probably a stupid question, but all I've ever used is virtual hosting (albeit with root access).

Oh, well when I only had my personal web site to worry about, I just ordered business class cable modem from my ISP. $99 a month including my cable TV and I get 1 static and 8 dynamic IPs and no upload cap (yeah right, then why've I never seen an upload faster than 80K per second? haha).

If you actually count on this web site to make MONEY then you want to colo that machine someplace. Ask around the requests forum for offers, or here for recommendations on a good place to house your server.