Put the shower pan in position so that it butts up against the wall studs and is centered over the drain stub coming up out of the floor. Use a pencil to draw the outline of the shower pan on your floor and remove the shower pan.
Mix up some of the thinset mortar in a bucket using the paddle attachment in the drill. Assuming the average size of 3 gallons for your bucket, you only need around a quarter of the bucket filled with the dry mix. Add water until you have a thick, creamy consistency.
Spread the mortar onto the floor of your installation area with the one-quarter-inch notched trowel. Move the thinset mortar across the floor in multiple directions, combing everything until you have an even layer of mortar distributed across the surface. Smear it up to your pencil lines.
Set the shower pan in place. Press down firmly with your hands across the entire bottom of the pan, applying your weight as necessary to ensure the pan is bonded with the mortar base. Make sure the pan is centered on top of the drain. Attach the drain of the pan to the pipe rough in and tighten it with your pipe wrench.
Mount the pan in place with the self-tapping screws. Drill through the flange into the wall studs, sinking the screws all the way down.
Place the backer board against the wall studs so that it overlaps the flange of the pan, further holding the pan in place. Install your tile on top of the backer board to finish the installation and lock the pan into the tile wall.