To Increase:
LIGHT ARMOR/HEAVY ARMOR: Go to the pause menu and lower the difficulty, then put 
on a full suit of whatever armor you wanna increase and let low level creatures 
attack you (rats, goblins, bandits, etc.). NOTE: if your armor in broken the 
skills will not increase, or if your fighting a human who is using their fist 
your skills will not increase.

ANY MAGIC SKILL EXCEPT DESTRUCTION: Simply use a low Magicka costing version of 
that spell (EX: Alteration use Protect, Illusion use Starlight, Resoration use 
Heal Minor Wounds)

DESTRUCTION: To easily increase your Destruction skill you must first have 
access to the Arcane University. Then go to the place in the University where 
you can make spells, then create a FIRE spell that does 3 damage on SELF, then 
cast the spell, it will hurt you but very little and your destruction skill with 
increase over time. NOTE: Have a supply of Healing Potions!