Remove the ceiling tiles from the existing grid by pushing up on one side then sliding the tiles out. Store the tiles out of the way as you continue the work.
Remove the crosspieces of the grid by pushing firmly up on both ends of the crosspiece. Store the crosspieces out of the way while you continue the project.
Unhook the wires from the runners of the ceiling grid. You'll probably need pliers to untwist the wires, or you can cut the existing wires with wire cutters and put in new wires when you rehang the runners.
As you unhook the runners, lower them down and place them out of the way.
Remove the nails holding the perimeter lip. You may be able to pull them out with pliers or a screwdriver.
In some cases you may need to use a pry bar.
Fill the holes left in the wall by the perimeter's nails with spackle, then sand them smooth when dry.
Measure the location for the bottom of the new ceiling. Snap a chalk line on each wall to aid in setting the perimeter.
Place the perimeter lip at the new desired height. Nail the perimeter into the wall at each of the stud points in the wall.
Replace the runners, hooking them to the wires and twisting the wires to hold the runners level. Check the runners with a level as you go along.
Snap the cross pieces back onto the runners. Replace the ceiling tiles to complete the project.