Cut the tip off a silicone caulk cartridge at a 45-degree angle with a utility knife. The cut will angle the tip to make a small opening in the cartridge.
Pull a caulk gun plunger backwards and place the cartridge into a caulk gun with the tip pointing down on the end opposite the trigger. Insert a large nail into the cut tip of the caulk cartridge to pierce the protective inner seal. Turn the plunger clockwise to engage the trigger of the caulk gun. Squeeze the trigger to start pushing caulk out of the tip of the caulk gun. Wipe the caulk off the tip of the cartridge with a wet shop towel.
Insert the tip of the caulk cartridge into the rear of the granite seam. Squeeze the caulk gun trigger slowly and move the tip from the rear to the front of the seam. Squeeze the trigger again when caulk stops flowing from the tip to form a continuous bead of caulk.
Wet an index finger with water. Wipe the seam with your wet finger from the rear to the front of the granite to press the caulk into the seam at the same level as the countertop. Wipe any excess caulk off both sides of the seam with a wet shop towel. Allow the caulk to dry according to the package instructions before using the countertop.