Push the old tile up to lift it off the frame. If the ceiling is painted, the tile might stick to the frame. Slide the blade of a utility knife between the frame and the tile to break the paint seal, if necessary.
Tilt the tile inside the ceiling space, letting shorter end pass straight down through the frame opening. Lower the tile and set it aside.
Push the shorter end of a new tile up through the opening.
Align the tile with the frame and set one short end on a short ledge. Hold the opposite end of the tile off the ledge. Lower the remainder of the tile into position on the ledge.
Tap up on any edge that doesn't seat properly on the ledge; let it fall down into position. Gentle jostling is usually all that is needed to help a misaligned ceiling tile rest fully on the frame ledge.
Measure a long and short side of the frame opening.
Measure a long and short side of a new ceiling tile. Mark the tile to match the frame measurements plus 3/8 inch.
Set a framing square on the edge of the tile. Align the angle of the square with the mark on the side of the tile. Trace the arm of the square across the tile with a pencil to make a straight cutting mark. Repeat at the mark on the perpendicular edge, if applicable.
Cut through the tile along the lines using a utility knife.
Raise one end of the tile through the frame opening, adjust it over the frame inside the ceiling space and lower it onto the ledge.
Set the L-shaped edge that you trimmed off the full tile onto the edge of the cut tile with the lip of the L resting on top. Trace the edge of the lip onto the tile to make a straight cutting line 3/8 inch in from the edge.
Cut down vertically through the traced line to a depth of approximately half the tile.
Cut through the edge of the tile horizontally to meet the vertical cut. Remove the trimmed section to reveal a new lipped edge.
Push the shorter end of the tile up through the frame. Turn it inside the space with the patterned side down. Lower the tile into the frame.