Use a 1/4-inch wood bit to drill pilot holes through the treated lumber that will be attached to the wall. Generally one screw every 24 inches is enough. Increase the frequency if the load will be heavy. Drill your holes centered in the lumber for good strong joints.
Chuck a 3/16 rotary mason's bit into your drill, do not use a hammer bit drill with a rotary drill. Wrap a piece of tape around the bit 1 3/4 inches from the tip. Have a helper hold the board in place on the wall and drill a shallow 1/8-inch deep marker hole through each hole in the board into the face of the wall.
Remove the board and drill pilot holes in each marked location to a depth of 1 3/4 inches as indicated by the tape marker you wrapped around the bit. Blow the dust from the hole.
Realign the board, with the holes in the board matching the holes in the basement wall. Install a tap-con style 1/4-by-3-inch concrete screw into every hole. Drive the screws in until the heads are flush.