To put in a new backsplash you will need to decide just which type you want. There is no need to put up any kind of backboard for this. Most home improvement stores sell prefabricated sheets of backsplash that look like everything from rock, tile to brick. These sheets are fairly simple to place on any wall.
If you choose to use these prefab sheets be sure to pick up some adhesive to bind it to your wall surface and caulking for the edges. Cut your prefab sheet to the dimensions of your wall, mix and spread your adhesive to the wall surface and place the backsplash. Allow it to dry to the manufactures instructions.
If you are feeling creative you could put in a tile backsplash. Here are some steps that will help you create that look you are looking for. Make sure you sand and clean the area you are planning to tile.
Adding a tile backsplash to the wall will mean that the outlets will be set to far back in the walls now so you will need to move them as well with electrical box extenders.
First you will need to turn off the electricity, remove the cover plates and screws. Slip the new box extender over the outlet, there is no need to undo any of the wiring. Once you have the new box in the wall, secure it and you are ready to begin tiling your backsplash.
It is easier to start at a corner so that you can use more full tiles, thus leaving the cut tiles for the edge of the backsplash. Use a pre-mixed adhesive that is mold and mildew resistant. You can find this at most hardware or home improvement stores. Keep in mind that this adhesive will dry much slower than a mortar will.
Cutting and Placing the Tile
You may decide to use a high end saw to cut your tile, however a low cost one will do the job just as well, if you take your time. Use all safety rules and keep your fingers clear of the saw.
Spread adhesive on the wall in a back buttering motion. Place your rows of full tiles in the layout, using spacers to help keep a consistent distance between them for the grout. Remember to remove the spacers before it dries in place. Give the tile a few hours to dry before you begin grouting it.
Grouting the Tile
Use a water based grout seal on the tile for easier cleaning and less chance of mildew and mold. Carefully fill in the joints with the compound, wiping off any excess overlap from the tile with a damp sponge. Once all of them are filled let the backsplash sit for at least 24 hours.