The easiest thing is to take it to a dealer or shop and pay to have the code read. Not every shop has an ABS reader, but many do. Most OBDII code readers do not read ABS codes, but some shops have special ABS readers.
One common problem with the Trailblazer is the ignition switch, and this is one of the few common problems that will affect both the ABS and brake warning lights plus the HVAC blower motor. (Look for the U1041 to show up on the ABS code reader.)
The other common problem is two problems really. One is the blower resistor that can be easily replaced, plus an unrelated ABS problem such as a wheel speed sensor.
If the ABS codes come out as C0201, C0265 or U1041, then it illustrates a loss of communication or voltage to the electronic brake controller. If it is not the ignition switch, then a likely cause is a poor ground connection to the EBCM.
(This ground is very easy to get at; it is under the frame on the driver's side, just in front of the front door hinge. There is a single thick wire terminating in a ring connector and bolted to a short crossmember of the frame. Once you crawl underneath, it is easy to find just forward of the front door. As one can see, it is quite exposed to the elements, and can corrode easily. The solution is to unbolt the wire, use a whiz wheel to clean the connector and the area of the frame it bolts to, reinstall the bolt and then spray the area with some rubber undercoating.)
My money is on the ignition switch.