Wall tiles can be installed over just about any solid, immobile surface, as long as the surface texture isn't slick or glossy. If it is, it will prevent the mortar that holds the tiles from properly sticking. This can be an issue if you're tiling over a painted wall. Gloss paints will be slick, and flat paints can be loose or flaking, causing other problems. You don't have to strip the paint off completely (in fact, it's better not to), but you do have to properly prepare the wall before you hang the first tile.
Run a wide drywall knife over the whole surface of the wall, scraping off any paint that's loose, flaking or bubbling.
Load a vibrating sander with 80-grit sandpaper. Starting at the top of the wall, run the sander over the whole surface, working your way across the wall and then down. Sand all grime and gloss off the paint, but don't sand the paint completely off the wall. Wipe off all the dust.
Divide the wall in half vertically, using a tape measure, level and pencil to mark it.
Use a notched trowel to spread thinset mortar on one side of the vertical line, near the bottom. Begin pressing the tiles to the wall, using the centre line as a guide and putting spacers between the tiles.
Build up and out from the bottom centre, spreading more thinset mortar as needed. Once all the full tiles are hung, measure and cut the tiles for the edges, using a tile cutter. Remove the tile spacers. Let the tiles set overnight.
Use your grout float to apply your pre-mixed grout from the top of the wall, pressing it into the lines between the tiles and smoothing it off the tile surface. After a minute, wipe down the surface with a damp sponge, removing the excess grout and smoothing out the grout lines. Let it set for two days.
Wear eye protection when cutting your tiles.