Well depending on how much he wants to get into it, there are advantages to having a decent GPU. I know CUDA is supported in some editing programs such as Adobe Premiere.
But as Blain pointed out, you can edit video on just about any hardware, it all comes down to how fast you want.
I'd recommend:
1 - a reasonably fast quadcore, ~3GHz
2 - 6-8GB of RAM, but definitely no less than 4GB (obviously a 64bit OS is inferred, Win 7 x64 unless you already have access to Vista x64 which would do just fine)
3 - at least
two 7200RPM or faster hard drives (avoid the "green" drives except for as permanent file storage), although three or more would be better
SSD changes the rules a little bit but if you're going with disc drives you definitely want multiple drives: one for the OS, one for your scratch/renders, and an optional 3rd for all your media file sources. You'll also want to avoid partitioning disc drives for a video editing machine.
here's a storage guide that goes a bit more into detail, but is also geared towards people intending to be relatively serious about editing
4 - a decently large monitor, 1920x1080 or 1920x1200. Multiple monitors can also help as editing programs can take up quite a bit of desktop space so you could keep a bunch of control windows open on secondary monitors to help keep you organized. Obviously if you can afford a 2560x1600 or 2560x1440 monitor that would be even better.
5 - a powerful video card is not needed, but can help if the software you are using supports it. Its not that common so make sure your software does support it before even considering it.
Another thing to think about is external connection options. It can be very convenient to have easy access to external hard drives, and thus you'd need decently fast connections if you want reliably fast direct access to such drives through your software editor. USB 2.0 is probably too slow, so you'd want at least eSATA or USB 3.0 connectivity. Firewire is going to be rare and probably too slow as well, especially relative to eSATA or USB 3.0.