How do I install a backsplash?

Do you have a preference? You will need to decide what type of backsplash and then you can get some great advice. Generally, if you are going to do tile for the first time make sure you choose a simple pattern. That's the only advice I have until you get a bit more specific.

What kind of backsplash? Wood, tile?

https://www.hometalk.com/search/posts?filter=backsplash

If you don’t want to commit to actual tile—or if you are not up to the task of cutting tile— there are tile sheets that actually are vinyl sheets that mimic tile/grout. The “tiles” are raised in the sheet, some of them have reflective backing which gives them a lot of depth like a glass tile. You can cut the sheet with scissors, peel off the backing and press into place. Make sure your wall is smooth and clean before you start and if you have painted you have to wait 30 days before applying the tile sheets. One tip is to rub the wall down with rubbing alcohol before applying the tiles. They don’t look as good as real tile when you look close but most people will not realize the difference. If you decide to use real tile and it’s glass, remember that whatever color is behind the glass may affect the final color so keep that in mind when choosing your mastic or thinset. The easiest products (thinset and grout) to use are premixed. They have a longer working time and sometimes more consistent color texture than what a newbie may achieve. It’s a good idea to buy a grout that has a matching caulk for a more professional finish. I ALWAYS lay out my pattern in advance on the countertop to confirm how the tiles will be affected by outlets and any other issues. Also that is a great time to double check the tile to ensure you don’t have different dye lots mixed together. I was helping a friend and her box of tile actually had two different versions of the same basic design. One group looked more grayish tan and the other looked more brownish tan. If she would have been just laying that tile without really checking, she might have not realized the problem until it was set to the wall. Once your new backsplash is in place, clean your outlets and switches and splurge on some wall plates that complement your new decor. Good luck!

This is a pic of the peel and stick vinyl backsplash I referenced in my previous comments.