Measure down from the existing ceiling to the level where you want to install the suspended ceiling. Draw a line on the wall around the perimeter of the room at this level, using a 4-foot level to be sure that your line remains level.
Install the perimeter cleat for the ceiling grid using the level ceiling line that you drew in around the room as a guide. This cleat is distinguished from the other parts of the grid because it is shaped like an L, while the other parts are shaped like a T. Screw the L-shape onto the wall so that the protruding part is on the bottom, using 1 1/2-inch-long screws.
Install T-shaped cross pieces by cutting them to a length that matches the length of the room using tin snips, then resting their ends on the lip of the L-shaped perimeter cleat. Position the cross pieces so that the spaces between them are equal to the width of the ceiling panels that you will be installing. Support the centers of the cross pieces by extending a wire from the cross piece up to a ceiling joist and screwing it to the ceiling joist. Check that all of the cross pieces are level and free of sag using a 4-foot level.
Insert T-shaped filler strips at a 90-degree angle to the cross pieces. The filler strips need to be separated from each other by a distance that is equal to the length of the ceiling panels that you will be installing. Install the filler strips by resting their ends on the bottom lips of the cross pieces.