Cassiopeia is one of my favorite champs to play with and is hard to master(not saying that I have). This build is very different from others you will see in that I don't focus on her abilities as much but focus on making her very hard to kill and dangerous.

PROS:

Good Harasser with her Q
Her Ult can turn the battle in your favor or save your/ally's ***
Can Farm very well
Good Spammer
Katarina's sister

CONS:

Not easy to play
Squishy
Mana is a problem early on
Her Ult requires good really good timing and has wide radius but low range

You'll want the magic pen runes to make your abilities moee effective. Mana regen so you can lane longer. Cooldown reduction coupled with your Mana Regen and Dead Cadence will allow you to maintain your dps(SPAM THOSE SPELLS!)

Normal 9/0/21 Lowered cooldowns on all skills and summoner spells. Exhaust and Flash upgraded. Utility Mastery for longer blue buffs.

Innate: Deadly Cadence

After casting a spell any subsequent spellcasts will cost 10% less for 5 seconds. This ability stacks up to 5 times.

Pretty much spamming your spells will make them cost less up to 50% less

Noxious Blast

Cassiopeia blasts an area with a delayed high damaging poison, dealing 75/115/155/195/235 (+0.9) magic damage over 3 seconds and granting her 15/17.5/20/22.5/25% Movement Speed for 3 seconds if she hits a champion.

Cost
35/45/55/65/75 Mana
Range
850

Get this first. It explodes near your mouse cursor and isn't does a certain amount of damage over 3 secs. For example if it did 30 damage it would do 10 damage every second for 3 seconds

Miasma

Cassiopeia releases a growing cloud of poison that lasts for 7 seconds. Any enemy that passes through it is poisoned for 2 seconds, dealing 25/35/45/55/65 (+0.15) magic damage each second and slowing them by 15/20/25/30/35%. Continual exposure renews this poison.

Cost
70/80/90/100/110 Mana
Range
850

Get at 1 point early on at least to help farm good. Also when attacking start with this to slow their escape. Most people ignore the poison but dont realize the slow. Also remember the cloud will grow. I like to use near an enemy so it will grow under them a lot don't notice that its getting closer.

Twin Fang

Cassiopeia deals 60/95/130/165/200 (+0.55) magic damage to her target. If the target is poisoned then Twin Fang's cooldown is reduced to .5 seconds.

Cost
50/60/70/80/90 Mana
Range
675

This is your nuke. SPAM this on poisoned opponents. Its almost instantly refreshed if it hits poisoned enemies.The effect works with other poisons i.e. Teemo

Petrifying Gaze

Cassiopeia deals 150/275/400 (+0.6) magic damage to all enemies in front of her. Enemies facing her are stunned for 2 seconds while enemies facing away are slowed by 60/60/60%.

Cost
120/160/200 Mana
Range
700

Use this in team fights or to start ganks. This is hard to use since its only really effective when they are facing you. What I do is flank them during a gank and get in front of where they will run so they go straight toward me then I stun.

Summoner Spells

Flash- Good to use get in position for your ult or escape
Exhaust- Good when you miss with or want to stack Miasma. Mastery adds MR debuff making your poison do more damage.
Ignite- When your poison isn't enough put this on to finish them

Meki Pendant +2 Health Potions Start with this so you can harass and stay in lane and 2 health potions.
*Tip: I try to have at least 2 health potions on me at any time especially during early/laning part of game they come in handy

Start building your Tear of the Tear will help you stay in lane longer.Don't be afraid to spam spells this will help with Archangel's Staff's passive . Then get this will make your spells do more damage. Now buy a this will give you a little ap and some more Cooldown Reduction spam spam spam spam. Time for you to get a this improve your spammability. Next build your Rylai's Crystal Scepter will make it almost impossible for your enemies to get away when used with Miasma and an extra 500 hp isn't bad. I prefer to start by buying Giant's Belt first but its up to you. Next get a Blasting Wand to start your Void Staff and eventually a . With this youll be unstoppable.

Alternate Items

Ionian Boots of Lucidity- If you really need max cooldown reduction although grabbing Blue buff is better
Mercury's Treads- If theres a lot of casters with CC then get this
can be switched for Morello's Evil Tome make sure you always have stacks
Will of the Ancients- Is an ok item, although the spell vamp is nice but i think there are better items that could be used instead
Rod of Ages- Isn't a bad item get Catalyst first for its great passive.
Lich Bane- Never used personally but have heard its good on Cass

Ionian Boots of Lucidity- If you really need max cooldown reduction although grabbing Blue buff is better
Mercury's Treads- If theres a lot of casters with CC then get this
can be switched for Morello's Evil Tome make sure you always have stacks
Will of the Ancients- Is an ok item, although the spell vamp is nice but i think there are better items that could be used instead
Rod of Ages- Isn't a bad item get Catalyst first for its great passive.
Lich Bane- Never used personally but have heard its good on Cass