Stir the ready-mix mud inside its container. Do not stir vigorously, since it needs to be smooth only. Vigorous stirring introduces air bubbles into the mixture, which cause the mix to dry quickly. Keep the container sealed when not using the mud.
Scoop some mud out of the container with a flat trowel and press it into gaps between the stairs and the Sheetrock. Press paper tape into the mud and cover it with a thin layer of mud. Use the trowel to smooth the tape down and remove any extra mud. Let the mud dry overnight.
Cover the tape with another coat of mud, extending 3 inches beyond the edges of the tape. Let this layer rest until it is dry to the touch. Smooth the mud with sandpaper so it will blend into the wall when painted. Paint the drywall with matte paint and let it dry completely. Glossy paint will not let the tiles stick well; you'd have to scratch it up so the tiles will have a grip on the wall.
Apply a thin layer of tile adhesive to a section of the drywall next to the stairs, using a putty knife. Work in sections since the adhesive dries quickly. Spread the adhesive on to the back of a tile and press into place on the Sheetrock. Space the tiles a little bit apart as you design your tile trim pattern on the wall.
Allow the tile trim to dry for 24 hours. Fill the spaces between the tiles with ready-mix grout. Clean off the excess grout with a wet sponge. Reclean the tiles when the grout is completely dried.