* OBD-II Scanner: This is the most common method. Your 2002 Silverado has a standard OBD-II port, usually located under the dashboard, often near the steering column. This is where you'd plug in a scan tool to retrieve codes.
* Paperclip method (for basic check engine light info): This only works to possibly check for a stored trouble code that's turning on the check engine light, and will not give you details about the code. It's unreliable and not recommended for anything beyond a quick check. It involves shorting out certain pins in the OBD-II connector with a paperclip (consult a wiring diagram for pin locations, it varies slightly by year and model) – this is generally not recommended as it's not reliable and can potentially damage your vehicle's computer if done incorrectly. An OBD-II scanner is far safer and more informative.
In short, the location you're looking for is the OBD-II port under the dashboard. You'll need an OBD-II scanner (available at most auto parts stores) to effectively read and interpret the codes.