Complete all the Mage Guild Recommendation Quests to be able to access the Arcane University. Purchase 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 choose 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, since you drain it from yourself to yourself. Cast the spells all the time while walking around or whenever possible. Your skills will increase fast 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.