The first step to replacing the differential in a Chevy Silverado is to identify which rear axle is under the truck. Differentials.com provides a breakdown of how to read axle codes as well as visual cues that help identify axles. General Motors axles, such as the common GM 8.5", GM 8.6" and GM 9.5", external visual identifiers will not be sufficient. DiffWizard.com allows users to input year, make and model of their vehicle and narrow down available rear end options.
Once you have identified which rear end is in your Silverado, to completely change the differential you also need to know if you have a factory-limited slip or open differential and the gear ratio. In all GM models, codes with that information can be found in the glove box, typically starting with the letter "G." Differentials.com, the dealer or differential specialists such as Randy's Ring and Pinion or Quick Performance can help translate those codes.
Local parts stores such as NAPA and O'Reilly's will have access to the parts required to change the differential in a Chevy Silverado. Companies that specialize in differential parts such as Randy's Ring and Pinion or Quick Performance also sell differential parts to the general public. When disassembling the differential, note the shin depth on both the carrier and the pinion as a starting point for the new setup.