Also, my method for easy skill leveling -
1. Register your demons in the compendium to ensure you can get them back later. Obviously, this will get real expensive if you're recovering powerful guys, so ideally you'll be getting your skills from trash demons you don't need anymore.
2. Fuse all the skills you want to level onto one guy.
3. Fuse him 'downwards' as cheaply as you can, the demon you put it on doesn't matter.
4. Go as far down as you reasonably can, since that'll make leveling quicker. It won't make compendium costs significantly cheaper since high level skills will influence that. I advise making your final destination demon something with only one skill to learn for simplicity's sake but it doesn't matter.
5. Once you've got your demon put him in your main party and go beat something up. You'll probably get multiple levels from this, once a demon learns all its skills it activates the 'whisper' prompt and your skills will level up.
6. Fuse him to the cheapest demon possible.
7. Go back to 5 and repeat until maxed.
8. After I was done I turned him into fodder for a high level special fusion, in this case a Jack Frost. So my King Frost got to inherit all those badass skills.
Remember some skills don't level up past 3, I've seen some that cap out at 5 (spirit drain), some that cap out at 8 (every normal damage skill I've leveled), and some at 3 (support skills).
This really doesn't have a huge effect other than reducing mana costs a bit and giving you a little extra damage. But I'm crazy and need to be the best.