When you install drop ceiling tile in your basement, along with forced-air heating and cooling, the duct work runs along the ceiling joists and pushes the air into the room through the ceiling. This setup demands that the heat registers be mounted on a ceiling tile. The difficult portion of this project is not the register's installation but placement. The hole you cut for the register must be centered underneath the duct's opening in order for the register to fit inside the duct and conceal the hole made in the tile.
Measure from the ceiling grid opening's front edge to the duct opening's front edge. Transfer this measurement to a ceiling tile, sitting face up on a hard surface. Make sure you measure from the edge of the ceiling tile that will be sitting on the grid's front edge.
Measure from the ceiling grid opening's left edge to the duct opening's left edge. Transfer this measurement to the same ceiling tile, measuring from what will be the ceiling tile's left edge. Repeat this step for the right edge and the back edge.
Use a level as a straight edge to connect the measurement marks you made in Steps 1 and 2, to form a rectangle or square on the ceiling tile.
Cut through the tracing on the ceiling tile with a utility knife, using the level as a straight edge. Lift the tile up into the grid. Center the opening underneath the duct's opening and lower the tile into place.
Place the heat register's opening through the hole in the ceiling tile and into the duct's opening. The heat register's cover plate should partially cover the tile's surface, hiding any imperfections made when you cut the hole.
Drive the heat register's supplied screws through the screw holes and into the ceiling tile to hold the register in place.