Press the corner tray into the shower at the intended height and ensure that it fits snugly. With a pencil, trace the edges of the corner tray on the shower wall.
Use a hand grinder to cut along the the traced lines through the tile to the backer board. You may need to cut deeper in the corner of the shower to reach the backer board.
Break the tile with a screwdriver and a hammer to remove the cut tile. Place the screwdriver perpendicular to the tile and hit the handle with the hammer until the tile cracks. Pry the tile out of the shower with the edge of the screwdriver.
Clean the corner tray and shower area with a damp rag to remove any dust. Mix the thin-set mortar and water to create a glue for the corner tray. Combine a half cup of thin-set mortar with four cups of water and mix until the solution is dissolved.
Using a brush, apply a generous layer of the thin-set solution to the backer board. Insert the shelf into the crevice and apply pressure until the solution dries.
While applying pressure to the shelf, use the damp rag to wipe off the excess thin-set solution before it dries. If you discover any dried excess thin-set solution later, chip it off with an x-acto knife.