Gathering the Tools
Before you begin, there are several tools that would be helpful to have on hand. A grout remover, hammer, ceramic chisel, and small, flat crowbar are extremely helpful. If the wall behind your tile backsplash gets damaged, you will also need a spackling knife and some plaster of Paris.
To get between the tiles in and the wall, you will need to start by breaking apart one tile. Begin by filing away at the grout surrounding one of the tiles with a grout remover or a small screwdriver. Next, using your hammer and chisel, make a crack in the middle of the tile and chisel away the pieces until the edges of other surrounding tiles become accessible. If you would like to preserve your tiles, go slow and be careful during this process.
One Piece at a Time
Once you can get to the edge of another tile, insert your small, flat crowbar between the tile and the wall. Your hammer can help you to wedge the crowbar in. Use the crowbar to pop the tile off of the wall. Some tiles in your backsplash may come off easily with minimal loosening. Others may require more effort to be pried off of the wall.
If the wall behind the backsplash is drywall, some of the paper may come off in the prying process. A concrete board will not have this problem.
A spackling knife is a useful tool for scraping off any remaining adhesive. If there are any dents or holes in the wall, plaster of Paris can help you to repair them. Be sure to allow adequate drying time before painting or putting up any new materials.