You must learn a special skill to tame plant beasts (Florafaun). It's taught by the tome, Trials of the Florafaun Hunter which drops from at least some florafaun rares in Harandar.
Forsaken hunters automatically know how to tame undead creatures. Hunters of other races must learn the skill from a Simple Tome of Bone-Binding which is a rare drop from miscellaneous Elite NPCs throughout Maldraxxus and its associated dungeons: Plaguefall and the Theater of Pain.
There are five devilsaur colours and five armour colours, resulting in 25 potential look combos! Sadly, only a few exist on beasts and none are yet tameable.