Summarize:

The wall needs to be smooth and clean before you apply the tiles to the backsplash area.  Take some time to inspect the wall where you will be applying the tiles to spot any damages that exist. You should patch holes in the wall with spackling compound or joint compound and then sand the surface if you spot damaged areas. Take mild detergent and water, and clean the walls.  You could use dish detergent. Remember that some adhesives won’t adhere to grease. You can also clean walls with trisodium phosphate and water. Look for this cleaner in home project stores. If you spot any oil or grease stains, clean those too. You can do so with a degreaser or a primer if a soft cloth with detergent doesn’t do the job. Let the surface dry before you continue with installation. Figure out where the tile is going to go before you actually apply it to the kitchen wall. Sometimes, it works best to center your tile around a focal point like a faucet.  Mark the start and the end point for the tile so you know how much you are going to need and where you plan to put it. Lay out the tile on the floor or on a large table to make sure the layout works, then measure it to be sure it fits the dimensions on the wall. Use tile spacers to account for grout. Put tile spacers in the corners of the tiles as you lay them to create even grout lines. Some smaller tiles have small protrusions called lugs that fit into the tiles next to them to create space for the grout. Grout is a mortar or paste used to fill the spaces between the tiles, giving it a finished look. Start with the spot on the wall that you can most easily see. Then, move outward and upward from that point. Use a level or straight edge to make sure the tile isn’t crooked. You might need to cut tiles if they won’t fit. A tile cutter will work for ceramic or porcelain tiles. Natural stone or thicker glass tiles may require a wet saw. Be very careful when using any cutting instruments. Purchase powdered thin-set mortar for natural stone mosaic tile. You will want to get this ready next. If you have ceramic or porcelain tiles, you may purchase mastic adhesive instead.  The mortar package will instruct you on how much water to put in the bucket, in addition to the mortar powder. Mix it. Mastic adhesive is often already mixed by the manufacturer. Let the mortar stand for about 5 to 10 more minutes, and then mix it again. Usually, you will only have a few hours to use the mortar after mixing it. Again, check the directions on the package. There are some mortars that you use right away after mixing. Again check the package for instructions as it can vary by brand! Many people suggest mastic adhesive glue for ceramic or porcelain tiles, and mortar for natural stone or other tile backsplashes.  Start spreading the mortar or mastic on the wall where you will place the tiles.  You will want to begin with a 2-foot section. Spread the mortar in a thin layer by using a trowel. Press it at a 45 degree angle. This method will make the mortar fully adhere to the wall. Now, use a notched edge of the trowel to add more mortar on it, and comb even ridges in one direction.  Working in small sections helps prevent the mortar from drying as you apply the tile. Use the trowel to apply mastic in similar fashion.  You will want to use the right trowel size. If you are using natural stone tile, you will want a notch trowel that is ¼ by ¼ inch in size. You may choose thinset/adhesive for glass tile instead or tile with adhesive on the backs.
Prep the wall. Pre-lay the tile. Prepare the mortar. Apply adhesive.