One of the last steps in tiling a backsplash is grouting the tiles. Although you can apply grout around the edges of the backsplash, the grout will chip and crack over time. Since the grout isn't surrounded by tiles on all sides, it would be exposed to damage. Instead, apply silicone caulk around the backsplash edges, using a caulk that matches the colour of the grout in the rest of the backsplash. It will look just like the grout, while lasting longer.
Stick a strip of masking tape along the counter where it meets the backsplash. Place a second piece of tape on the backsplash, parallel to the first piece. Place tape on either side of the joint where the backsplash meets the cabinets above in the same manner. Repeat for the sides of the backsplash if you didn't use bullnose tiles.
Place the tube of caulk in the caulking gun. Cut the tapered tip of the tube where it is approximately the width of the spaces between the masking tape.
Apply a bead of caulk to the spaces between the masking tape. Fill the joints, but try not to overfill them.
Place a damp rag over your index finger. Run the rag over the caulk joint, pressing the caulk into place, smoothing out the surface and removing excess caulk. Switch to a clean part of the rag as it gets dirty.
Pull up the pieces of masking tape slowly and carefully so that you don't get caulk on the backsplash tiles or the counter. Let the caulk dry according to the manufacturer's instructions.
If you use bullnose tiles on some of the edges of the backsplash, those edges don't need any caulk or grout because those tile edges are finished.