Mark the mounting hole of the curtain rod brackets onto the wall with a pencil. Measure and position the brackets as indicated with the instructions for your curtain rod to determine where to mount the brackets.
Install a drill bit that is one size smaller in diameter than the plastic anchor you are using. Drill holes at each of your marks on the wall.
Insert the closed end of the plastic anchor into each of the pilot holes. Tap the end of the anchor with a hammer or the back of a screwdriver handle until the anchor is flush against the wall.
Place the curtain rod bracket against the wall, lining up the mounting hole over the end of the plastic anchor. Screw the mounting screw into the plastic anchor with a Phillips screwdriver.