We all know the art, but the man is something of a mystery, as he keeps himself out of the limelight. While this section here is meant to enlighten you about him, writing up a biography that mostly draws on other people's information seems dull to me, so I'll point you elsewhere for that for the time being. For now though, here's a couple of older interviews with Shirow, with Toren Smith's focused more on Shirow's current works(at the time), and the Dark Horse one turning out something of a mini-autobiography in looking at his background, influences, and some techniques.
Over the years Shirow has employed a variety of tools and techniques to craft his art. While he's heavily into CG coloring and rendering his backgrounds in 3D these days, he spent much of his career working with pen and paper, where his core style saw the most evolution(though some call his jump to computer assistance the biggest evolution his style has undergone). In an old issue of Comikers magazine, dating back to 1995, he walks us through his process of creating an image, as well as giving us a look at the various tools he uses to draw out his art. Unfortunately, the specifics and whether or not he uses a computer for it at all are lost on me, as I can't read Japanese and no one's ever made a translation of it that I can find. Still, it gives a good look at all of the steps he goes through, so you can glean some information from that, presuming you can get ahold of it.
Most of Shirow's early work was drawn with pen and pencil, and colored with color pencils and alcohol markers(Copics?), along with an occasional foray into acrylics. In addition to these more traditional methods of creating art, Shirow also employs some rather unusual processes, notably he often makes the point about using his photocopier with various everyday items(as mundane as the static sheets you throw in the dryer) to generate textures to incorporate into his imagery, which is something fairly unique to Shirow from what I've seen. In the Toren Smith interview above, Shirow lamented upon the fact that his favorite pen, an odd 'turnip-shaped' design, was no longer being made, leaving him to find as many as he could for future use and seek out potential replacements(as well as going into some more details about the paper and processes he uses).
As stated before, he does much of his work on the computer now, doing little more than sketching his initial character art and scanning it in before jumping into Photoshop and Lightwave3D for everything else with it. Initially his computer work seems to have been done primarily on a Macintosh 9600/350 with older versions of Photoshop and Corel Bryce, along with some Lightwave 5.5 and Cinema 4D. In Intron Depot 3, he notes on one illustration from the very end of 2001 that he had moved to Lightwave 7 and went through the process of that illustration with the manual in hand. At some point, he also upgraded from the 9600, to a 933MHz G4 mac on OS 9.2.1, perhaps around the time he made the jump to Lightwave 7 and Photoshop 7. Pure speculation on my part, even though that setup seems nice enough, it wouldn't be surprising to me if he'd moved into the wonderful world of OS X, particularly as the notes in Ballistics notes are a couple years old now and there are very few developers are working on non-OS X Mac software.
Update - Well, I guess I stand corrected, according to the Animerica interview listed above, he's still on essentially the same setup as that in Ballistics, no OS X for Shirow yet =(