In my hondas, there's a two pin connector by the ecu that you jump with a paperclip and the check engine light will flash a given amount of times. Check the code vs. internet code listings and you have your problem.
In modern GM's, they put a multi-pin connector in the wiring harness; in almost all GMs it is located below the steering wheel near the top of the steering column. The code reader simply plugs right into it, and the little digital readout on the code reader will show you the last code stored in memory.
I have found that sometimes the internet code lists are not 100% accurate, so I just call my local dealer's Service Dept and explain to them that I have a code reader and they have always been great about looking up my codes in the GM Service Manuals for me.
And yes Vin, those are the code readers. That is a cheapo one, I'd consider spending about double that in order to get one with a digital readout, they are
much less confusing to read than those little LED ones.