ESD Is very real.
If you don't ground yourself, you are likely to irreversible damage the computer.
Michael above, has the wrong idea.. I wouldn't be taking my computer to him to be fixed!
You cannot see ESD damage, but it literally blows 'holes' through circuit boards on a microscopic level.
We all know how tiny circuits are.
If you 'zap' a board, you wont know about it- it can be very hard to diagnose why the computer is acting up in a strange way.
You might blame software, drivers or an incompatibility for that BSOD, or just say 'that computer part is just a dud', very few blame ESD.
At my work, we always use ESD protection;
I work on Mac- we use esd wrist strap (to take away static from our bodies) connected to an ESD matt to take static away from the mac, which are then connected to a ground outlet. We use a air filter/ polariser (i might have the wrong terminology) to even take moisture out of the air (moisture can conduct static through the air).
We clean the matt with a special spray every day to ensure it remains esd safe.
I can't however share much other knowledge on how to set it up properly with grounding etc, other than to say 'be careful'...
I wish iFixit would create a whole kit (esd Mat, strap, a grounding plug (to make it easy to ground! spray and maybe even an air filter)... and a set of instructions - it'd clear the air a little on how to set up.