$1000 is easy to build a high end gaming system with. If you forgo the "fancier" stuff, you can easily build something up that will do you justice. I'll start my recommendations now, but there's likely someone else doing the same thing, so check this thread in a bit, you'll probably have a ton of recommendations.
As for a cost aspect, I tend to side with AMD - I know the platform best, and you can really get some amazing deals with them. Intel is good, but $1000 is a little harder to work with. As long as you don't mind being "upper high end" instead of "teh highz end" then you can do well with AMD. Someone who knows Intel better will post, so weigh the options when you see them.
I know you're asking about how to build one, but I felt it important for you see some parts that would work well together so that you could get an idea of what all you would need to make a functional system.
(Motherboard + CPU)
Total Cost before shipping: $977.91 (Shipping to me ended up being $14.35, so it was still under $1,000, all total at $992.76)
You can go with a lower end video card (like a 5770) to save some scratch, but that system will handle just about anything you can throw at it.
Assembling a computer is not much different than putting together a puzzle or building legos if you ever did that. If you don't like a part here, ask for an alternative and we'll help out. Once you have a setup you'll like, order the parts, and use YouTube, as FBJ suggested, to help you build. Building your own computer is a great way to save money and it gives you a sense of pride knowing that YOU put the system together. Essentially building a computer means putting the parts in the case, using supplied parts (the case will come with the parts necessary to mount the motherboard) and then attaching everything to the board. Processors, Video Cards, RAM all go in only one way, and have great manuals to show you how to do it. Approaching a new computer build is cake, don't let it become daunting to you. There are a ton of great resources out there, this site included, to help you finish the project.