Successfully complete all the Mage Guild Recommendation Quests to gain 
access to Arcane University. Then,
buy the cheapest spell you can find for each of the magic based skills 
(Illusion, Conjuration, Alteration,
Mysticism, Restoration, and Destruction). For Destruction, a Drain Spell is 
recommended. Go to where you
make your own spells and select a spell. Make it so you only use up 1 
Magicka and the spell is on "Self".
Name the spell and create it. Do this with all the other types of magic 
based skills then make them all on
"Self", including Destruction. If you used a Drain spell, when you use it on 
yourself it may appear you
took damage but you do not, because you drain it from yourself to yourself. 
Cast the spells all the time
when you are walking around or whenever possible. Your skills will increase 
quickly without having to
wait between spellcastings. Note: This trick will only work if the spells 
are cast on "Self". Spells do not
count towards experience unless they have an effect on something.