I do not know if it is xbox that is complex (I do not consider it complex- in some ways I consider some of the higher end wii stuff to be far more fiddly and annoying) but that is besides the point.
Two classes of original xbox hack each with two main methods of achieving it.
1) Hardmod
a) Chip - you buy in a chip. Not sure what ones are still available right now but they are available for all models.
b) TSOP - only for 1.0 to 1.5 models (the last was 1.6) and can be done with fairly basic soldering.
2) Softmod
a) game exploit - I forget which games but you can search (I mainly used splinter cell). Here you copy a hacked save* to your xbox (see softmod installer deluxe or Krayzie NDURE), run the game and follow the on screen instructions.
b) hotswap - locking (mentioned below) is removed for a very short period during boot. You have your xbox open and ready for this and remove the hard drive at the right moment. With the drive unlocked you inject all the relevant hacks and carry on with life. This needs no games or special hardware though it is not without risk (though will have to try hard to damage your xbox and the instructions are simple enough).
*you can get the save on there in a variety of ways. 1) you make a USB adapter (the original xbox controllers are USB by any other name so it involves soldering four wires to each other) and inject the save onto that (still quite possible but getting more annoying as the years go on as modern USB drives tend not to work well) 2) you get an action replay and copy the save onto a memory card 3) you get an already hacked xbox and copy a save onto a memory card via it.
With the game exploit method you will probably end up at a basic hacked dash, most people change this for XBMC as XBMC runs all the games just as well and is a great media player (it does not do H264 that well but it is otherwise up there with a PC and probably better out of the box than most PCs are).
With one important exception both lead to the same results and can all run the same code (there is no "you can only run this game if you are chipped"). The important exception is hard drive replacement- the xbox has an internal hard drive (more on that in a moment) which is tied to the system by a seldom used feature of IDE called locking. Being seldom used not all IDE hard drives support locking, perhaps more annoyingly nowadays is that IDE is not on all motherboards so you might need a slightly older system to do some of it (the USB to IDE adapters will not work). Being a useful thing to do though we have a nice list of hard drives that have been tested and what happened to them-
http://xboxdrives.x-pec.com/?p=list I would suggest you find confirmed to work from that list although if you have an old one from a PC then by all means give it a go (if it does not lock then it does not lock and you have merely lost the time taken to test it).
Mod chips and TSOP do not have this worry and can accept any hard drive.
The xbox comes with a hard drive, for most purposes it is considered to be about 8 gigs in size although later models had 10 gigabyte drives (you will have to format the drive to gain the extra 2 gigs though) with a bit under half that available for general use (part of it taken for system files, part for games to use and part for other stuff).
You can play commercial xbox games from the hard drive or from the DVD drive (after hacking you just burn isos or you can build multigame ones). There are no external options available (no network save for homebrew things and no USB worth a damn).
The original hard drive is enough to play quite a few games although the DVD drive is capable of playing dual layer discs (somewhat larger than the maximum free space on a stock drive) which some games did use the full amount of without being able to be reduced in a useful manner. This leads to people wanting to change the hard drive for a larger one which has been covered already, to do this most people use a custom linux distribution aimed solely at fiddling with xbox hard drives called xbox HDM. To use xbox hdm you need the xbox hdm download and a copy of your xbox EEPROM file which holds all the relevant data to lock drives to work with your xbox.
Original xbox games come in iso format (albeit not the standard PC style one) which you need to extract the files from, I already took programs to do it with the big two being "C-Xbox tool" and Qwix. To get them to the hard drive once extracted from the iso most people use FTP (a well liked file transfer protocol) to send it across the network and as most hacked dashboards run FTP servers (password and username both xbox for most of them).
As an aside most xbox homebrew was built with Microsoft's own SDK that was leaked which means distributing it is not like most other homebrew, you can download a program called auto xbins to get at it though although I recommend having a copy of auto installer deluxe (you have to burn it to a disc) which has pretty much everything like emulators, homebrew and dashboards on it and can install them just by you asking.
After that the only real thing of great note is xbox linux but we can cover that later.