there's a few ways to go about it.
1 - If you want to host a LAN party game, just install the game in however many PC's you have in your home/work network. It's loads of fun when playing against co-workers.
2 - Find a game server host. There's a monthly fee and it depends mostly on however many slots you get and the location of the host. I'd recommend you the one we use right now but I won't. For one thing and one thing only; it's not for beginners. If this is your first time starting off, I'd suggest
www.gameservers.com Not too expensive and very easy to setup. Just a couple clicks away and off you go. Whereas the servers I have, I gotta do quite a few things before they are up and running.
3 - Do you use Linux? If so, there are Linux files out there that you can technically run from your home PC or use an extra PC and use it as an actual server just to run CoD. You need a decent amount of upload speed to have a good amount of people before people start to feel lag. I've been meaning to try this out myself for the heck of it but like everything, I have no time. For this, you don't necessarily need a super PC. Just upload speed, a decent processor; mainly a decent PC and you should be good to go.
That's pretty much what I know. Let me know if you need more info or explain something in detail.