Sand the ridges where the pieces of wood were originally joined, by using a short, firm scrubbing motion. This is to remove old glue and any dirt that has built up on the wood surface. Run a thin line of wood glue inside the ridge where the wood pieces meet, put the pieces together, and use either clamps or weights to hold the pieces together until the glue dries completely.
Turn the drawer upside down, and unscrew the old plastic track slide by turning the screwdriver counterclockwise. Position the new track slide directly over the screw holes and replace the screws.
Turn the knob on the hand plane, setting it to a thin depth, if the drawer is sticking. Pull the drawer back and forth a couple of times, paying attention to where the drawer and dresser frame are rubbing, so you know which area of the drawer is swollen. Remove the drawer, position it with the part that sticks facing you. Put the plane against the drawer, and applying light pressure, begin to rub in smooth strokes that follow the grain. Replace the drawer. If it does not stick, you are done. If it still sticks, remove it and plane the wood again.