Info from Kabam on Hero skills on the forums.
Skill List Edit
Skills are divided into Common, Advance, Rare, and Epic. Each level is more powerful than the last and usually has pre-requisites from the last.
Hero Skill Enrollment Edit
An unlocked skill can be enrolled (aka applied or assigned) on a hero. Daily free enrollments are random, chosen from skills unlocked in the Library. Using an Enrollment Letter is also random, but increases the odds of better skills. Using a Skill Book allows enrolling of a specific skill on a hero.
Each day, 1 or 2 free enrollments may be used in each city on a hero. An empty slot can be chosen, or an existing slot can be replaced.
One a skill is enrolled, other slots may get that same skill. The skill will stack. It's implied that skills listed as Unique in the Library can only be enrolled once per hero.
Free enrollments reset at midnight, Middle Earth Time.
Effects on Legendary Heroes Edit
Most, perhaps all, of the skills have additional bonuses to Legendary heroes based on the Grade (I, II, III, etc) of the legendary hero. These bonuses are generally smaller than the overall bonus by a good margin. For instance, a Grade 5 Legendary hero will get 0.2% extra attack power decrease from Broken Bows. Compare that to the level 1 debuff of 1%. These bonuses stack, just like the skills will stack.