Most of the HVAC parts we're interested in are located behind the dash, which makes this job somewhat unpleasant. Later S-series models (like my 2004 Blazer) were redesigned so the actuators could be accessed without removing the dash. Unfortunately for me, I had to do some dash work to get at the Sonoma actuators.
The process begins with removing the many plastic trim pieces which conceal the underside of the dash. The best way to do this is to get yourself a 7mm socket driver (or better yet, a cordless drill with a socket adapter) and start unscrewing. If you're smarter than me, you'll carefully segregate all of the screws and bolts, label them in Ziplock baggies, and take a bunch of digital photos. When the job is done, you won't remember where they all go...trust me.
All the under-the-dash plastic came out, as did the trim around the instruments. I removed the radio, the heat and A/C controller, the ash tray, and the glove box door. The last two components might not have needed to be removed, but I was doing this for the first time and wasn't sure.
It's important to disconnect any electrical harnesses that may interfere when the dash is moved. The GM designers were kind enough to allow the dash to pivot forward for access to the components behind it. This is nice, because the whole dash can remain in the vehicle for this job. However, if there's not enough slack in the wires, some of the harnesses may be stretched when the dash pivots forward. Disconnecting some of the harness clips is tough to figure out, but a small flat-blade screwdriver and a set of metal picks helped out greatly. A small retractable mechanic's mirror is also helpful, as it's difficult to see behind some of the harness connectors that must be disconnected before certain trim pieces can be removed.
Once all the trim pieces on the front and underside of the dash are removed, the defroster grille and the dash speaker covers must be removed. My Sonoma had 4 metal screws under these grilles which secure the dash to the firewall. The defroster grille is tricky - this is one of the most commonly broken pieces of dash removal. The grille is held in by several metal clips and must be carefully pried out.
Most of the various S-series owner websites have "Stickies" in their forums that cover dash removal procedures. These are often contained in heater core replacement discussions, where the entire dash has to be removed from the vehicle. The website I gleaned the most info from was the now defunct ZR2USA.com, which was focused on the ZR2 version of S-series vehicles (like my Blazer).