Most GSPs will allow you to rent servers on a monthly basis. They will all want money up front, payable by online methods, typically credit card or paypal. That might need a responsible adult

. Most shared servers will be available within only a few minutes of payment as it's automated.
Make sure you understand if you are renting branded or unbranded (costs more). If branded the name of the server will need to include the GSPs own tag ie. "GSP >> my server name"
Although the service may only be for an initial month they will auto renew so make sure you understand how to cancel.
Most GSPs for CoD4 will provide a control panel that allows you to set your own configuration. These are essentially a set of text config files. A set of default files will exist. Not every thing can be tweaked if you want the game to be ranked.
If you want to run your own maps, rather than the supplied game maps then you have to run the game in a modded fashion. You will also need some webspace or the GSP will need to provide somewhere for fast downloads to the gaming computer. Setting up custom maps can take time as there is a lot of uploading to both the game server, and the downloadable webspace.
The arrangements for specific operation and config of a server are best discussed via the GSP's own support forums. they'll often have help guides for setup of many of the games.
If you are in the UK, make sure you go to a provider with UK servers. Nothing worse than lag due to the thing being too far away.
Amongst others try looking at
http://www.inx-gaming.com/game-servers/,
http://www.killercreation.co.uk/game-servers,
http://www.multiplaygameservers.com/