Remove the ceiling tile where you want to install the recessed light.
Place the can for the recessed light onto the tile and trace it.
Cut a hole in the tile with a utility knife.
Install an extra hanger wire in each corner of the beams around the tile you removed. This will provide extra support for the lighting and bracing.
Measure the distance between the inner edges of the beams, and cut two 2-foot by 4-boards to match.
Place the tile back into the ceiling.
Place the 2-by-4s on top of the tile, one on each side. Connect them to the beams by lifting up the edges of the adjacent tiles and driving 2-inch screws through the beams and into the end of the boards.
Slide one of the adjacent tiles out of the way so you can access the inside of the drop ceiling. Install the light by placing the can over the hole and extending the brackets for the can far enough to reach the 2-by-4s for support.