when you have "q"w"e"
when you start to engage an enemy champion you must use your w that will grant you move ment speed and dps dmg then the e who will dmg and reduce the armor of the champion then finish with the q for maximal dmg .

@lv6 start with using "W" just before ulting since when you use your ultimate you will fly over the enemies and dmg then with knowback a your " w " when in the dragonform( ulti) your abilities will have a bonus more of a team fight passive then use your q while your infront of them and then finish of with a "e" if you want .

Well the cooldown i sverry important for shyvana for example if you use your q and w you can spam your w how much you want when fighting and that makes shyvana good dps dmg . and with the frozen malet you will have slow and when they are runing away from you you will just keeep follow them since you will have unlimited w (dps dmg )