Clean the backsplash area well to remove any grease, dirt, or stains. If desired, paint with a similar color to the tile in case there are any gaps.
Measure the height between the countertop and upper cabinets in several places to check for any slope. Also check for level on both surfaces. If you have a slope, the best place to minimize its visual impact is right underneath the cabinets.
Lay out the tile prior to putting on a wall and make sure it fits together as desired. Peel the backing off and stick the wall firmly. I prefer to do all the whole tiles and then come back to the cut areas.
For vinyl or silica tiles, heavy duty scissors or snips can be used to cut them. For glass or stone peel and stick, glass snips and a wet saw will be used for intricate cuts.
Add a line of caulk around the perimeter where the countertop meets the tile to prevent any moisture from getting behind the tile.