This cassiopeia build is highly based on Furber's (used to be 1st rated) guide, with like... one change from yours truly. I'm only making this build to redirect others towards his archived one, similarly titled "Cassiopeia - There's a Snake in My Boot". I suggest, if going to play Cassiopeia, that you read this archived and truly awesome build. Using it, I've won many games. I will only add a cheat sheet, and a few thoughts on the character.

Pros
Great farmer
Great damage
Can dominate any lane if played correctly
Not too hard to learn
She's a snake!

Cons
Squishy
Often targeted
Ultimate is difficult to aim effectively

Cassiopeia is slightly squishy with no burst, instead she focuses on DoT's. You must learn to aim your Noxious Blast accordingly, as it is required for your main damage, Twin Fang. You can also use Miasma for Twin Fang to proc it's 0.5 CD, and really any poison will do it, but Miasma only stays in one place, and most move out of it (even at level 3, where it does almost no damage, they'll avoid it. Use this to your advantage). Learning to aim Noxious Blast is key, but it's the same with Miasma. Miasma is a great farming and slowing skill when aimed correctly, and can be key in ganks or teamfights. Just pop a Miasma behind the champ-to-be-ganked, throw in a Noxious Blast and start hittin' him with Twin Fang over and over again.

For runes, I go for Magic Penetration Reds and Quints, to make her hit harder with everything she does! I go with mana regen (per level) yellows because she does have some mana issues, even with tear of the goddess, if you're farming and harassing accordingly. I don't go with flat mana regen, because I find per level works better late game. I go with cooldown reduction blues, because even though she has a 0.5 cooldown on her Twin Fang, you must have a Noxious Blast to get that 0.5. Noxious Blast might have a short cooldown, but why not make it shorter, allowing you to harass and farm more?

I go with a simple caster mastery build, speccing into most of the mana regens, cooldown reductions, ability power increases, and upgrading Flash because it is a very reliable summoner spell.

For Summoner Spells, I roll with Flash and Ignite, because Flash is a personal favorite. It goes very well with your ultimate, and is always useful when running away. I go with ignite because she already has two DoT abilities, why not throw in another? Besides, what if you're going against Mundo or Swain. They get so cocky when they have their ultimates on. Prove them wrong, Ignite, Ultimate, Miasma, Noxious Blast, then spam Twin Fang! (always put Miasma on your ulti'd target).

Cass's Noxious Blast is effective early and late game, I've had it hit for about 900 damage late game (with all of my core items, of course) as well as it gives you a bonus to movement speed. Who could ask for more? Use it often, whether farming or harassing, or both! (if the enemy likes to sit near their minions) Miasma doesn't hit very hard, but is very useful for running away, farming, or chasing. Pop it on the back creeps, behind the enemy champion to slow them, or infront if chasing! Mixed with Noxious Blast, this skill will let you chase any champion, or run away! Twin Fang is her most reliable damage, seeing as it hits relatively hard, with a 0.5 cooldown to (There's a Snake in my) boot! (If they're poisoned, gotta spam those Q's, folks!~) Her ultimate is a relatively hard hitting, difficult to aim, but very effective stun. Seeing as you could stun an entire team with correct aiming and conditions!

Cass can be a terrific farmer mid and late game, just pop a Miasma and Noxious Blast on the minions in the back, while auto-attacking the minions in the front. Once Noxious Blast is off CD, pop it on the minions in the front (if the ones in the back are dead).

Cass's ultimate can be key in 1v1's to 5v5's, but is a huge pain learning how to aim. If the enemy champions are smart, they'll just turn around when you get too close. Use this to your advantage, continue getting closer, slowing them with Miasma and hitting them with Noxious Blast for a speed boost, then flash infront of them and quickly ulti behind you. Hopefully you'll hit them and then kill them, or you'll just miss and be sad. When faced with a 5v5, you don't want to go out in the thick of it, you'll just die. So try and flash in, aiming correctly, and ulti. Try to get all 5, it's hard. XD After that run out and start DPSing. It can also be used when chasing (I don't recommend it) or running like hell. Just wait until they're close enough and ulti them, which you really should because you have a slow and speed boost, why would you need anything more?

Well, I don't consider this an actual guide. More of... A few thoughts on how to play her and a directory to the real guide, which I base most of these ideas on. The real guide is right here, http://www.mobafire.com/league-of-legends/build/cassiopeia-theres-a-snake-in-my-boot-40430

I highly suggest if you read this guide, to read that one first. Have fun and don't play a bad Cass! (I cut myself when she's free.)