Basically, I have the quiet casting, bow spamming assasin. But, I want to spice things up with some Fury or Calm spells. Can I get some tips?.

hit them from a distance with fury and watch them kill each other

Hit them with fury and watch the death match begin. Sneak attack the winner.

This^. It's always fun. Followers tend to F-up fury spells though.

Fear: the most underrated of the Illusion spells. If you can somehow be sure that an enemy won't be able to run away and attract even more enemies, then Fear is the best combat related Illusion spell there is in terms of what spells are available to you early on in the game (and even in the middle stages). This is because they don't fight back until the spell wears off. That's not the case with Calm and Fury. Nope, they just cower in the corner while you lop their dome off. It's also the best way to escape a situation where you're about to die because you end up putting max distance between yourself and the enemy. They run one way, you run another.

Calm is solid and the Pacify spell is excellent. Pacify is an area spell that calms several people at once. So cast it, pick out the first guy you want to kill, and the others will stand around and just watch. But you can't buy Pacify until you're have a score of 75 or better.

Mayhem is the ultimate spell in the entire game. It's a Master level spell that's Fury³. Stand off a long distance, like when a bow shot is kind of far, cast it and watch the fireworks. It's really great but so OP you need to use it sparingly.

I hate how enemies stop fighting each other the second the fury spell wears off.

Instead of utilizing hit and run tactics, Illusion spells bring that fight back into your favor when used correctly. Say you are cornered and getting hit will be inevitable. Use that calm spell to control the enemies mind, either drop back into stealth OR get the advantage of opening up on the enemy from a distance.

So I would break it down like this:

Frenzy spell: if there is multiple enemies to engage, this spell is your friend. It will take one of the two targets out of commission so battle will be more in your favor. If they do not kill each other through one frenzy spell, dps the lower healthed enemy and calm the other, restealth and open up with a deadly sneak attack or distant shot from your bow.

Calm spell: I like calm because it gives me a chance to get away and open up from a distance. Also another VERY effective use for the calm spell is, once they are subdued by the power of the spell, you can walk further into the dungeon to see if there are enemies farther up the way. This is where Fear can come in handy.

Fear Spell: This spell is useful and not used as much due to lack of knowing its potential in combat. If there are two enemies that happened to detect you and you're unable to get away, You can fear one enemy so he gets out of the combat entirely while you take out the other target or targets, this ensures that the feared enemy has to travel back to the combat zone which takes time, this is better then the calm spell because they can break free of their calm if they are hit with anything, fear makes sure they aren't around to do that.

Good luck.

The Calm spell says "Creatures and people up to level 9 won't fight for 30 seconds".

Does this work on draugrs? My level 5 character tried it on some and it didn't do anything.

Untill you get the Master illusion perk which allows illusion spells to work on the undead, daedra, automatons. You cant.

Honestly illusion is probably the most overpowered skill in skyrim if you put the perks into it. Frenzy is great to make enemies kill each other while you can hide in invisibility to reduce the chance that you'll be spotted. Calm is useful if you get spotted by your enemy. You can easily calm an enemy, and then sneak up behind them for an easy backstab. Fear is great against boss-like opponents that you can't one shot with a backstab. You can relentlessly hack at you enemy over and over again while he cowers in fear. Also illusion will not work on undead, daedra or the non-living (draugr, vampires, dwemer constructs, dremora) unless you have the master of the mind perk which I believe requires 90 illusion.

Correction, Master of the mind being unlocked at level 90 Illusion.

I love being hidden and using throw voice to get all the enemies in an area grouped up and then hitting them all with frenzy. The resulting mayhem is pretty funny. For fun place bets on who you think will come out on top.

Have a good aim

I would say fear is probably the most underused and there's a good reason for it. Fearing someone and having him run off half through the rest of the dungeon and alerting every other thing in there to your presence is an adverse effect. Use it wisely.

Sometimes its good to rile up the whole dungeon if your trying to clump everyone together to get by a AOE frenzy spell.

Calm even works as a combat pauser so yu can get a better shot in. If they see you, use calm, they will walk away, take back your stealth status, and finish them

Illusion is ridiculous at high levels. I'm playing a PURE illusionist, NO damage through any other means, and now I'm at a high enough stage for my spells to affect undead, daedra and automatons, it's just too easy. At low levels, it was pretty hard, but now I just mayhem everything, then calm the victor. Either that or I use frenzy on the most powerful enemy, like the bandit chief or the centurion master, and it usually kills everything else or everything else kills it, so it's a win-win.

We call that the Puppetmaster

Use the calm spell if you don't feel like fighting those assassin and thief. They don't like it but it works.
At my last play through which I was playing a mage, you know that nordic ruin has that bridge going over the river near Whiterun, you have that bandit that pulls up for a toll. I always calm her then have others in her clan start shooting arrows at my character.

In Riverwood, there is a kid that annoys me, so I done a fury spell on him which it did not work and this woman start to attack my character. I done a calm spell on her and she did not like it.

Is that really possible? How do you get rid of bosses?

That is a good question. If there is any others around the boss, use frenzy, If you are inside cave, mine are a ruin, use traps. Don't about outside. Hope there is a bear near by or a troll.

Well fury is great to put everybody in a frenzy and have them attack eachother while you pelt them with arrows from afar. I find calm is is useful when you wish to get out of a dangerous situation or you can use it to reposition yourself and get a better vantage point. Fear is best used to make it easier for you to flee if need be.