This is a loosely built guide. I recommend that you read my guide as well as this one, http://www.mobafire.com/league-of-legends/build/introducing-cassiopeia-to-competitive-scene-152382. Mine is more of an ideal of how to play Cass. Depending on who is opposite you in mid, whether they have a jungler, how your team is built, all these things will change how you must play cass. I will list times to change playstyle below, I am still working on this since I am slow right now and will update this over time.

Any notes, changes, or advice you have are welcomed, please rate and comment.

It is recommended that if you are new to Cass that you use Cleanse. I still use it, it is a must because of her squishyness. She can easily be killed in the 2 seconds of one stun. That and flash will save you life. I dislike ghost because her q already is the same if you hit an enemy champ and her w is a slow, so she normally doesn't have escape problems in the long run.

NEVER TRY TO JUNGLE, until at least level 6. The golemn buff is really useful, but the monsters are not nearly as good as minions.

Champion Spotlight: http://www.youtube.com/watch?v=neQNvEyuhPU

The items can be very loosely ordered. I suggest getting the Deathcap early so you can kill minions faster. The Crystal scepter is also a must for both offense and defense, buy the giants belt first or else you will have a very hard time. Cass is one of the squishiest characters in the game, and if you don't move quick, she will simply be dead. Note that the runes, masteries, and boots give you a nice amount of magic pen early on, so you will be fine until later. The Void Staff and Abysal Scepter are not really necessary unless they are stacking magic resist, but it is nice to note that the Scepter's range is larger than any of her abilities, so fear not.

If the enemy is dumb and doesn't stack magic resist, feel free to buy the deathfire's grasp instead. It is a nice powerful hit that will make some fights go faster.

Fear not the banshees veil, for your q will pop anyone in it's range and will be up again in 3 seconds. If you really need to hurry, use w which won't pop it and then e which will be back up in 0.5 seconds.

Not Used and Why
Chalice of Harmony: I used to get this, I don't anymore because the tear is much better for mana needs and it is equally as cheap.

Kage's Lucky Pick: Another one that I used to get. It offers a small amount of ap early game as well as extra gold, but since Cass doesn't have much money problems, it really is not necessary.

It is a pain getting all the money required for those expensive mage items. Luckily, Cass can clear a group of minions in about 6 seconds while getting each kill. The plan is simple, run up to the minions and use q on the most clustered group. Throw w on the other group. Later on, this will kill them, so you can just leave, unfortunately until then you will need to finish the job. Very easy and simple, but I thought I would note it.

Start out with the sapphire crystal. use your q when to slowly drain enemy health over time. Try to use it when they are by minions to damage them as well. keep their health around 50% until you get fangs at level two, then when they start to run due to low health, go all out on them with flash to chase if needed. As soon as you have the money buy the tear. Then spam your q. You need to have the mana for later. Mana potions aren't bad if you feel like it. When you get to level 3 on you q, start to focus minions with it. You should hit groups of three mages twice to kill. This is best for getting gold. The Crystal Scepter is crucial for escaping, this is why you should keep your w on cooldown. The slows compound to a very high amount (like 50%). Use it and you q quickly to escape any enemy champions that are too close. I prefer to save her ultimate for group fights, but it is great for escaping. The real advantage to Cass is that the damage occurs over time, so people think they can win when they are already dead. This build stacks on AP very quickly because of the speed at which you can kill minions. This makes you go from pinger to nuke. It is very easy to move at a group fight from the side and kill 3-4 champions in 2 seconds.

Hit with q until they start to run, never move in until it is clear that they have no chance. Throw w in front of them, spam e and q. Remember to be careful not to use e when they are not poisoned or else you will probably lose them. Save you ult for ganks.

Move in quick, hit before they see you. Use q first to get movement speed and lower cost. Throw w behind them to make retreat impossible. Spam q and e on the squishiest first, then move to tanks. Keep in mind to not move anywhere near any crowd control users. If you can, pop from behind, throw q use you ult when they turn, throw w under them and then spam e.

You will die. Always have that thought in you mind. Cass is someone who can chase like a boss, but don't do it for long. A stun coming from behind will destroy you. You need to use her for a while before you can have quick reflex accuracy with your q. Always keep this movement buff up. Your ultimate will save you more times than you can count. Cass is not a lax character who can walk into the middle of a group fight and watch everything die. She does that from a decent distance away. And if they run, then they have no chance. Against other casters, open with your ult and use everything. If you can't kill Annie or Ryze before they cast then you will be dead.