Here's a breakdown:
Un:
* General negativity: This is used to create the opposite of the word it precedes.
* happy -> unhappy
* important -> unimportant
* lucky -> unlucky
Une:
* Vowel or Silent "h": This is a grammatical rule to maintain a smooth pronunciation.
* happy -> unhappy
* honest -> dishonest (Here, "h" is silent)
* able -> unable
* employé -> unemployé (French word starting with a vowel)
Exceptions:
* Words starting with "h" that is pronounced:
* hero -> unheroic
* historical -> unhistorical
* Some words have both variations, with slightly different meanings:
* unbearable (too much to bear) vs. unebearable (not able to be borne)
Remember: While these rules are generally true, there are some exceptions. If you are unsure, consult a dictionary or a grammar guide.