Clean the area where the caulk will be going with alcohol and paper towels to remove any debris.
Tape off the edge of the counter and the edge of the backsplash, leaving only a small strip (approximately 1/16 of an inch) of untaped area where the caulk will fit. To do this you may apply the caulk and cut away a small strip in the seam with a sharp, ergonomically correct utility knife.
Apply a thick bead of caulk into the seam. You do not have to worry about being careful, as the tape prevents the caulk from going elsewhere.
Run your finger over the caulk to press it into the seam and ensure an even bead of caulk.
Pull away the top piece of tape at a 45-degree angle.
Run your finger back over the caulk.
Remove the bottom piece of tape away slowly-but-steadily. Removing too quickly can result in pulling away your caulk.
Run your finger smoothly over the bead of caulk one last time. This final rub will smooth out any ledge created by the tape. Inspect the caulk line to make sure there are no bumps; smooth out any bumps in the caulk.