The daily quests count as the training. You can actually go out and tame all 6 mounts at once, though you may have to log off / log back in to get the next taming quest to show up (unless they fixed it). Then you'll get a daily for each, and after you do enough dailies you'll be able to learn the mount permanently. I only have 2 finished, but I assume once you get all 6 done you'll unlock the tier 3 stables plans.