Remove the old caulk with a utility knife. All of the old caulk needs to be removed so that the surface is flat and clean.
Tape the backsplash and the wall. Leave a quarter inch free between the tape where the caulk will go.
Apply caulk with a caulk gun to the open area between the strips of tape. Bead out the caulk slowly and do not over-apply.
Smooth out the caulk with the bottom of a spoon or a knife. This will give a professional look to the caulk. You can use a finger, but a spoon will provide a smoother finish.
Remove the tape immediately. Leaving the tape on while the caulk dries will cause a permanent bond.