The easiest way is to find someone in your city who'll do it for you. Check Craigslist.
If you want to do it yourself, you need a few items:
One of the hackable games: Splinter Cell, Mechassault or one of the James Bond games (I forget which one exactly). You need an original edition, as the bugs have been fixed in the "Platinum Hits" versions.
You'll need an Xbox memory card to put the hacked saved game on with a Linux bootloader.
You'll need a way to connect a Xbox controller to your PC. The memory card goes in the controller and you can then copy the 2 files to the memory card. I use a special USB adapter.
Getting all of the above cost me about 25$ total on Ebay, shipping included. The best part of doing it this way (called a "soft mod") is that you can do any number of boxes (I've done 9 so far) without having to open them up. It's also 100% reversible.
The modding part involved copying the 2 files (hacked save game file + Linux bootloader) to the hard disk, starting up the game and loading the hacked file. The Xbox crashes, the LED goes red and after a few seconds, a new dashboard comes up. You can then FTP to the box and install whatever you want (Xbox executables only of course).
I usually install the latest version of XBMC. Upgrading the hard drive is also a good move, since you can then copy games to it and run everything from the hdd. It's not a requirement, but not having to get up to change games is a major plus, let me tell you. Even if you keep the original HDD, you can stream movies, music and photos from any PC on the network (using any numbers of protocols) and run games and emulators from DVDs.
Going from stock Xbox to a modded one with XBMC installed and booting up takes about 10 minutes.
Replacing the hard disk involves opening the case (obviously) and can be done in about one hour.