The commander usually stays with the cavalry reserve, ready to strike at the flanks, guard the rear or as a last resort, fill in a spot where the lines broke. Usually, generals/lords/kings avoided fighting themselves when they were middle aged or older, but as young men they often participated for glory and more often to raise troop morale. They did pick their fights though, if they could, and charged in after the enemy had been softened up.
Communication happened trough horns/fanfares, which were then interpreted by the lower ranking commanders and translated in to verbal orders, such as "advance" "charge" "retreat" etc. Flag waving was usually used for morale purposes more than anything else, as the large battle standards were very heavy and mounted on T shaped poles. Flag signals could be used when making a silent ambush or attack however.