Training up your spells and abilities used to be fairly complex -- not the process itself, mind you, but figuring out where to go. Trainers were tucked into obscure nooks and crannies all over the world, a real incentive to go exploring. Several infamous profession trainers were even located inside instances; you had to fight your way in, bags stuffed with all the mats for the next batch of recipes you hoped to train, and skill up like mad so you could buy the next available recipe while your group kept the area clear.
Training is much simpler in today's World of Warcraft, but it's hardly intuitive. We've pulled together a few notes on training for class spells and abilities, professions, riding skill for mounts and weapon skills, to help steer you to the right place at the right time.