Mark the location of the left and right stringers on the joist. To do this, first mark the location of the first stringer for the left side of the staircase and hold the level up against the joist. Adjust the level until the air bubble is dead center in the glass tube to indicate the level is perfectly straight up and down. Run the marker along the edge of the level to make a mark on the joist. Follow the same procedure to mark the stringer on the right side of the staircase.
Measure the width of the staircase to determine the positions of the other stringers, if necessary. There will need to be a stringer no more than every 16 inches to provide adequate support for the stairs. For example, if the staircase is 32 inches wide, you will need a stringer at the center point between the two stringers. If the staircase is 40 inches wide, you will need two stringers in the middle of the staircase to stay within the 16-inch span limit. In that case, you would place a stringer every 13.3 inches along the joist. Once you calculate the spacing for the stringers, mark their locations following the same steps you used to mark the locations of the stringers along the sides of the staircase.
Place first angle bracket against the joist so it lines up vertically with the marking you made on the joist. Use the lag bolts and washers to secure the angle bracket to the joist. Tighten the lag bolts with the socket wrench. Lift the stringer so the edge is tight against the joist, then use the lag bolts and washers to secure the stringer to the angle bracket. Now that the stringer is held in place on one side with the angle bracket, place another angle bracket on the other side of the stringer and attach it to the stringer and joist with lag bolts and washers.
Install the remaining stringers by following the same procedure. However, before securing the additional stringers to the angle brackets, place the level across the stringers to makes sure they are level. Raise or lower the stringer you are installing until the bubble in the glass tube is dead center in the glass tube, then attach it to the angle bracket.