Pull the drawer out of the drawer cavity, and ensure there is nothing obstructing the drawer in the cabinet. Sometimes a pan or pot handle from the cabinet below the drawer is extending into the drawer pathway.
Check the drawer track to make sure there are no protruding screw heads. Tighten any screw heads with a screwdriver.
Slide the flush drawer back into the drawer cavity. Make light pencil marks on the face of the drawer where it overlaps the drawer opening.
Pull the drawer out and place it on a flat surface. Sand the edges of the drawer where it overlaps the opening with a sanding block and fine-grit sandpaper. Swollen drawer fronts usually only require a small amount of sanding to get the drawer to fit flush into the drawer opening.
Push the drawer back into the drawer cavity and test the fit. Repeat sanding if necessary.