Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Cassiopeia is an excellent early game harasser and a great source of sustained damage for the entire game. She is good at escaping, chasing, and kicking *** in team fights.
I like to build Cass with a lot of health because two of her moves, her Twin Fang and her Ultimate, require her to be quite close to the enemy. As such, you will probably be taking a bit of damage. You have Flash to escape and distance yourself from the combat zone, and Exhaust to save yourself from an enemy DPS or to finish the kill on a fleeing enemy. Will of the Ancients is a great item to heal yourself up with, to stay in fights, and to survive in situations where you normally wouldn't; I find myself getting this sometimes depending on the match. Also, if you are getting a lot of kills and enemy doesn't seem very good, you should pick up a Mejai's Soulstealer after the Archangel's Staff and then probably skip Rod of Ages. Deathfire Grasp synergizes with her other abilities quite well; depending on your playstyle, you may want to pick this up as well for the damage and reduced CD on your ult.
I level Noxious Blast (Q) first because in my opinion it is one of the best harassing abilities I have ever seen. It seems to have a slightly bigger radius than Lay Waste (though this may not be true) and it does a lot of damage, and it is better than Lay Waste in the sense that it does not have reduced damage if you hit more than one unit with it. On an enemy squishy, Noxious Blast will take away 10-15% of their health on hit. It does similar damage to Twin Fang but you don't have to get close with the enemy to land it.
I get one point in Miasma early game for the aoe slow. It isn't a great source of damage and you already have Exhaust.
Twin Fang will be your main source of damage in Cassiopeia's combo mid-late game. The idea is obviously that you want to poison the enemy with Noxious Blast and then spam your Twin Fang which becomes a .5 sec CD if it hits a poisoned enemy. If you miss the enemy with Noxious Blast, you can simply hit them with Miasma for the poison debuff. Depending on the situation you may want to start with Miasma anyway just to lay down some slow. It's pretty simple.
The full combo is:
And so on. Add in your ultimate when it is appropriate.
Your ultimate, Petrifying Gaze, is an amazing ult when you can position it correctly but not too useful if you can't. On activation, you deal a bunch of magic damage (also applies the poison debuff) and stun enemies in a cone who are directly facing you and slow those who are not. The problem is that your ult is very finicky when it comes to who is facing you and who isn't. If you get lag, or if your opponent knows that you will be using it, or in big hectic fights, you are not likely to stun with it. In team fights, you may get 1-3 stuns depending on how lucky you are and the skill of the enemy team. However, once you DO land your ultimate, it's pretty much lights out for whoever you hit with it (unless you're using it to escape). Use your combo of death on anyone stunned by your ulti is pretty much dead, since you deal so much damage.
As I mentioned earlier, Cassiopeia is not only squishy, but her full combo requires that you are close to the enemy. Not only that, but if your enemy retreats, then there is not too much you can do about it since you do not have any (reliable) hard CCs. (This is why I put Exhaust in the build.) Therefore, you must be very careful to not overextend yourself into enemy territory because you will be tempted to get close with the enemy to get the kill. Especially in the early-mid laning phase, you must be patient with her. A good combo to use is Flash+ Petrifying Gaze on an enemy champ in your lane with low HP. He is guaranteed to be surprised, and you can finish him off with your combo.
Cass is very good at escaping and running away. Use Miasma for the slow and then Noxious Blast to speed yourself up. You can do the same when you are chasing someone. Just remember to keep spamming Twin Fang; the rythm of the .5 sec CD can be hard to get into.