Spell Vamp on Cassiopeia is like no other. She benefits from Spell Vamp more than any other champion. With her single-target E spell being her main source of damage, it replenishes health with sufficient spell vamp just like an ADC would with life steal. Not to mention that aside from spell vamp, her E already heals on hit 6/8/10/12/14/16 (+ 10% AP). When you are near full build, you will have 800+ AP, so 10% plus the base heal is already around 90 health. Add 26% spell vamp to that and you'll heal ((90 + (.26(150 + (800*.55))) * 0.5 [this assumes the opponent has 100 MR after all of your magic penetration which is unlikely unless they are a tank, so you'll probably do even more than this] ) or 120+ health per E, not even adding on the health you are getting from your Q and W spell vamp procs.

Cassiopeia builds a stack of Aspect of the Serpent once every 6 seconds (10 times per minute) and for every second that an enemy champion is poisoned, up to a max of 500 stacks.

100 STACKS: 5% increased ability power, and Twin Fang now heals for 6/8/10/12/14/16 (+ 10% AP).
250 STACKS: 10% increased ability power and 25% bonus cooldown reduction.
500 STACKS: 30% increased ability power.

Passive - Aspect of the Serpent
This is an amazing passive that in the late game can give you over 900 AP.
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RANGE: 850 | COST: 40 / 45 / 50 / 55 / 60 MANA | COOLDOWN: 4
*After 40% CDR, its cooldown is 2.4 seconds.
Cassiopeia hurls poison at the cursor's location, which strikes after a 0.4 second delay. All enemies within the 75-radius area are poisoned, taking magic damage over 3 seconds.
Cassiopeia gains 20% bonus movement speed for 3 seconds if Noxious Blast damages a champion.

MAGIC DAMAGE PER SECOND: 25 / 38.33 / 51.67 / 65 / 78.33 (+ 15% AP)
TOTAL MAGIC DAMAGE: 75 / 115 / 155 / 195 / 235 (+ 45% AP)

Q - Noxious Blast
This spell is mainly used for harass early game. Before you engage someone you should try to land this on the enemy, so you can make sure they are poisoned for your E ability spam. If you are trying to escape, this spell can help since it gives you 20% increased movement speed if you hit a champion with it.
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RANGE: 850 | COST: 40 / 50 / 60 / 70 / 80 MANA | COOLDOWN: 14 / 13 / 12 / 11 / 10
*After 40% CDR, its cooldown is 8.4 / 7.8 / 7.2 / 6.6 / 6 seconds.
Cassiopeia throws a growing cloud of poison to a target location, granting sight of the area and growing from a radius of 125 to 250 over 7 seconds. Enemies in the area are poisoned and take magic damage per second for 2 seconds. Continual exposure renews the poison.

MAGIC DAMAGE PER SECOND: 10 / 15 / 20 / 25 / 30 (+ 10% AP)
MAX. MAGIC DAMAGE: 90 / 135 / 180 / 225 / 270 (+ 90% AP)
SLOW: 25 / 30 / 35 / 40 / 45%

W - Miasma
This spell is mainly used as a zoning technique during the laning phase. You can put this down and make your opponent miss some CS or predict their movements easier since they can only move in a limited direction without stepping into the poison pool. Aside from zoning, this spell is great for waveclear since it allows you to spam your E consistently. This applies to engagements too as it helps peel opponents off you and applies poison to them for your E. The vision granted by this spell should also be noted and thus gives this more utility in checking bushes. In conjunction with your Q, this spell can be used during an escape by providing a slowing barrier that opponents have to walk around or through.
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RANGE: 700 | COST: 35 / 45 / 55 / 65 / 75 MANA | COOLDOWN: 5
*After 40% CDR, its cooldown is 3 seconds.
Cassiopeia fires fangs at an enemy, dealing magic damage and applying a stacking debuff that amplifies further poison damage by 20%. Stacks twice for a maximum of 40% amplification. If her target is poisoned, Twin Fang's cooldown is reduced to 0.5 seconds.
If Twin Fang kills the target, refunds its mana cost plus 3% of her maximum mana.

MAGIC DAMAGE: 55 / 80 / 105 / 130 / 155 (+ 55% AP)

E - Twin Fang
This spell is what makes Cassiopeia amazing. This spell is your main source of damage, sustain, and utility. At 100 poison stacks, this spells restores health and, with the spell vamp you get from your runes and items, it grants you massive lane sustain. Once you get a Hextech Revolver, all of your opponents' poke will be nullified by the amount of health restoration you gain by using this spell to farm. With the recent buff which increases poison damage by 40%, you should always remember that while you are spamming your E to kill your opponent, you should be using your Q and W to add more damage. It is recommended to smart cast this skill.
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RANGE: 825 | COST: 100 MANA | COOLDOWN: 120 / 110 / 100
*After 40% CDR, its cooldown is 72 / 66 / 60 seconds.
After a brief delay, Cassiopeia blasts all enemies in a 80º cone in front of her with her gaze, dealing magic damage to them. Enemies facing her when damaged are stunned for 2 seconds, while enemies facing away are slowed by 60% for 2 seconds instead.

MAGIC DAMAGE: 150 / 250 / 350 (+ 50% AP)

R - Petrifying Gaze
This spell allows you to kill most of your opponents before they can even react with its 2 second stun. With its low cooldown, you can even use this for wave clear. This spell will win a team fight if used correctly. It is also great for escaping if your Q and W failed to peel the enemy off of you. Flashing Ults are a great way to surprise your enemy for an easy kill.

+ Late Game Hypercarry
+ Can kite once Rylai's is obtained
+ Amazing AOE 2 second Ult Stun for Team Fights
+ Amazing harass during laning phase
+ Surprisingly good duelist because of Spell Vamp
+ Can solo dragon when enough items are acquired (usually after Rabadon's)
+ Amazing Baron Damage (Cannot solo because of lack of mana)

- Easily ganked
- Low Mobility
- Outranged by other AP Carries

Flash: Definitely needed as it is your only escape.

Exhaust: This spell will be the only thing that saves you from burst champions if your ult fails.

Early Game:
Pre-6
You are extremely squishy as an AP Carry early game. Especially since you do not have Rylai's yet, your spells will not kill unless the opponent fully commits since the enemy can escape your range easily. You should focus on harassing for poison stacks and farming with your E for Tear stacks and mana. Never engage unless you have enough mana and you are sure you can get a kill. Be wary of engagements and make sure you use your exhaust. Never push lane. You will die if you get ganked.

Post-6
Now you can engage confidently and push a little harder since your AOE stun (if used properly) can handle a 1 v 2. If your opponent gets trapped in your W (Miasma), spam your E as much as possible. This will eat a lot of their health away. If your lane is pushed and you find yourself with a lot of mana (perhaps from blue buff), then you can farm the jungle safely due to your spell vamp.

Mid Game:
By now you should have your Rylai's, which gives you immense utility. If you don't think you can catch an opponent with your Q, hit them with E to slow them down, then follow up with any spells. Your spell vamp is formidable and gives you great dueling potential. If you are behind, don't despair because if you don't feed extremely hard, you will win once you hit late game.

Late Game:
Now, you are a hypercarry. Most lone champions will run once they see you (or at least they should). You should be able duel anyone if you have enough mana. You can solo dragon and duo baron (with a full mana pool, you should be able to do around half of Baron's health). You will carry the game now.

Preferred:
Tear of the Goddess
I prefer this build instead of the Rod of Ages build because this gives more mana and more AP. The more mana you have, the longer you can commit to an engagement. Building mana instead of building mana regen allows you to spam your spells consecutively to secure a kill. Also, the more mana you have, the more effective your E mana restoration effect has. By the the time you max your Tear, you should have around ~2,000 mana. 3% of 2,000 is 60. So every last hit you get from farming with your E will give you 60 mana. The completed item (Archangel's Staff) also helps protect against burst champions with its mana shield.

Hextech Revolver
Spell vamp on Cassiopeia is different from spell vamp from any other AP Caster. This is because no other AP Caster has sustained damage from a single target spell that they can spam. Having spell vamp on Cassiopeia is similar to having life steal on an ADC.

Rabadon's Deathcap
I prefer to get this after my main utility items because what's the point of doing massive damage if you can't catch your opponent (Rylai's slows them down and boots increase mobility)? Spell vamp early on is essential for sustain. Not to mention that by the time you buy this item, you will have near 500 stacks. So, pretty much you get +60% extra AP once you buy this item.
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Not Preferred:
Zhonya's Hourglass
I don't like this on Cassiopeia because usually even if you do activate this, you will still die due to your low mobility and lack of effective escapes. The armor and AP is good, but not as useful as the AP you get from Rabadon's, the utility you get from Rylai's, the mana you get from Archangel's staff, the penetration you get from Void Staff, or the spell vamp you get from Hextech.

Liandry's Torment
I find this item most useful on poke champions that whittle down the enemy's health like Xerath. The extra damage you get from Liandry's does not compare to the damage you get from the other listed items.

Armor in General
I don't prefer to buy armor on Cassiopeia because I think the spell vamp is enough to cover your health needs. Fed ADC's usually don't stand a chance against you because if you stun them with your ult, they die. Also, since Cassiopeia has percent increases to AP, I think its best to maximize the amount of AP you have to get the most bonus percent increase.

All in all, I believe Cassiopeia is a strong, sustained damage champion that unfortunately does not appear in games as often as she should. She is a little difficult to play with her skill shots that require good prediction, but once you have it down, you will be unstoppable. I believe with her kit as it is now, she is still a competitive champion even after her rework.

Thanks for reading this guide. I hope it helped you.