You don't need to do anything to cause an increase in height during puberty because the inevitable influx of hormones that occurs during puberty naturally causes an increase in height. However, boys typically take a couple years to catch up to girls.
A healthy diet is important not to stunt growth at any point during the body's maturation phase. Many mothers remind their kids of this when cajoling them to eat their vegetables. However, diet alone does not start or cause growth in height, which is the role of chemicals released by the pituitary system, including HGH, thyroxine and calcitonin, which spurs growth in the muscles and skeleton.