I've just started a new char and I'm trying to raise my illusion magic. I only have one spell at the moment, clairvoyance. But when I use it my stats don't increase, I have the Mage blessing and the well rest bonus, which means I should be 25% quicker at leveling up. I don't understand why this particular stat is increasing.

Clairvoyance doesn't increase it. You need to pick up fury, calm, and the like. Eventually you'll get muffle and that will probably give you the most.

Yup once you get Muffle use it all the time in a dungeon. It only increases when you're near/around a creature and can threaten you I think.

OK well that would explain it. I didn't realise that certain spells didn't raise your stats.

Nope you can cast muffle whenever and it will raise your illusion, by a lot. You can train illusion very fast with muffle.

That's not true. Clairvoyance raised my illusion several levels when I was using it. Your skills go up based on how much Magicka you use when you successfully cast. Clairvoyance uses a small amount of magicka over time, so it takes a lot longer to go up. Muffle is a much better choice though.

I just pay trainers. It encourages me to go out adventuring and dungeon-diving rather than sticking to quests only. As an added benefit, when I am adventuring, I use illusion (among other trees) a bit and that levels it up a bit more.

Mufflespamming is ridiculous for leveling illusion. The whole idea to prevent abuse falls apart when all you need is one spell to become a master illusionist.
Telekinesis works great for alteration, by the way.

Spam mufle wherever you go and you'll get illusion to high levels in NO time at all. Make sure you get the magic cost reduction for the appropriate level. I think its an apprentice level spell.

P.S. Illusion is an amazing school to invest into, turns the toughest fights into a chaotic battlefield.

That Muffle spell works a treat, don't suppose there's any good ones for alteration?