Cassiopeia is AP Caster which controls the battlefield and requests diffriend combos and quick hand.
Those are her skills:
Petryfing Gaze(Ultimate)
Cost: 120 / 160 / 200 Mana
Cooldown: 130 / 120 / 110 seconds
Magic Damage: 150 / 275 / 400 (+0.6 per Ability Power)
Slow: 60% (at all levels)
Twin Fang:
Cost: 50 / 60 / 70 / 80 / 90 Mana
Magic Damage: 60 / 95 / 130 / 165 / 200 (+0.55 per Ability Power)
Miasma:
Cost: 70 / 80 / 90 / 100 / 110 Mana
Magic Damage: 25 / 35 / 45 / 55 / 65 (+0.15 per Ability Power)
Slow: 15 / 20 / 25 / 30 / 35 %
Noxious Blast:
Cost: 35 / 45 / 55 / 65 / 75 Mana
Magic Damage: 75 / 115 / 155 / 195 / 235 (+0.9 per Ability Power)
Movement Speed: 15 / 17.5 / 20 / 22.5 / 25 %
Movement Speed buff lasts 3 seconds.

And those are her Pros/Cons

PROS:
-Noxious Blast,Miasma,Petryfing Gaze will allow you to catch up or escape anybody.

-Noxious Blast can be good scout tool,Cast it in brush that you suspect your enemy is,if you get your speed boost you will know enemy is inside.Same thing with stealthed enemies.

-At level 3 you can start using your endless combo:Miasma,Twin Fang,Noxious Blast,Twin Fang,Noxious Blast,Twin fang

-Your Deadly Cadnece should solve your mana problems at early game

-Sexy voices

Cons:

-Easy target in teamfights

-Requests mana build late game

-Cant carry gamme

Addonitialy Cassiopeia can you jungle.
Start with Miasma followed by Twin fang.
Keep creeps iside Miasma and keep using Twin Fang.
Start with Elix of Fortitude and 3 health potions.
Dont drink Elix of Fortitude right away,first clear wolf,ghoul and 2 golem camps then recall and buy Elix of Brilliance.Go to Blue Buff drink bot elixes,make sure you have atleast 3 health potions and get your buff.
Start ganking around level 4.

I take typical caster runes:
-Magic Penatration marks(They are definitivy the best)

-Cooldown Reduction Seals(Far best as i can get from Seals)

-Flat Ability Power Glyphs and Quintessences

You noticed that i dont like "Per level" runes.Its becouse im trying to cover all items in early game so i get fed then nobody will care about late game.You gonna be just fine..

Masteries:
9/0/21
Taking magic penatration in offense.
Movement Speed,Cooldown reduction,More XP and gold,Improved flash in Utility.
I dont take anything in Defense becouse champion like Cassiopeia doesnt need anything defensive.

-Start up with Dorans Ring.Its definitivly best item for Ability power mage casters.

-Take Boots of Speed.Dont rush Soceress Shoes right away becouse Cassiopeia already has many chasedown and escape abilities.First take Atmphying Tome after boots then upgrade Boots in Socerres Boots.

-Atmyphing Tome followed by Blasting Wand and Giants belt upgrade to Ryalis Creystal Scepter.Ryalis Crystal scepter gonna make you less targeted becouse of your huge health.It will ensure you clean escape or catch up enemies.

-Zhryonas Hourglass is definitvly item that you need the most.Great ability power improvmance good armor(you dont really need armor)but generaly its Active:Passive,allways be ready to use it.

-Rabadon Deatchap-3 Words: HUGE ABILITY POWER.
Cassiopeia needs it

-Archangels Staff-Deadly Cadnece wont be doing all mana babysiting for you.Its time to do it on your own.Archangels staff is great item for it.Even though if you deside you need more survability grad Rod of Ages instead.

-Abystal Scepter:Gives me ability power,magic resistance and whats the best its lower enemies magic resistnace.As you may noticed i only have runes and Soceres Shoes for my Magic Penatration so grabing Abysall Scepter to reduce it is good.If your enemies are mostly AD grab Haunting Guise instead.But if your going well with both ad and ap casters/dps dudes grab Voids Staff.

Best Choises:
Ignite(For easy killing)
Heal(Savior)
Flash(Mobility)
Ghost(Mobility)
Less viable:
Clarity(Big mana problems)
Exhaust(Having troubles with big enemy damage)
Smite(If you want to jungle)
Unwanted:
Rally(AD ON CASSIOPEIA?-Facepalm)
Revive(TANK CASSIOPEIA?-Facepalm)
Claviyorance(SUPPORT CASSIOPEIA?-Facepalm)

-Akali-Use Miasma in Twilght Shroud if shes trying to hide followed by Noxious blast.

-Alistar-Dont let him harras you.Use max range of Noxious Blast to make him stay back.

-Amumu-Stay behind minions so he cant stun you.

-Anivia-Avoid Flash Frost(Its easy)Move out of her ultimate by grabbing Noxious Blast movement buff first to escape it faster if your in middle of it.If you by the edge move out regulary.

-Annie-Stay away when she reaches level 6 if you dont have Flash ready to use.

-Ashe-Stay behind minions so Volley hits them instead of you and if she is trying to send arrow to other lane warn your allies about that.

-Blitzcrank-Stay behind minions so he cant grab you.

-Brand-Avoid his Pillar of Flame and Sear,stay away from targeted allie by his ultimate.If your his ultimate target stay away from all your allies at it can bounce to you mutiple times.

-Caitlyn-Move out of range of Ace in The Hole if you can,if you cant you can flash out of it or move to place thats unavailible to her for vision.Try to avoid Piltover Peacemaker.

-Cassiopeia-Move out of Miasma atleast 5 steps away.After setting down spell turn around(After level 6 or at level 6)So she cant stun you.Move alot so she cant harras you using Noxious Blast.

-Cho'Gath-Move out of his EarthQuake thingy,dont go to close as he may attempt to silence you.
Keep him away from minions so he cant grow.

-Corki-Avoid his ultimate,move out of his gun thingy that when you activate there are bullets in front of him,dunno how its called bla bla...using Noxious blast and Miasma or if its life case flash away.

-Dr.Mundo-dont try to harras him once he has ultimate active and try to stay behind creeps so his axe hits them instead of you.

-Evelyn-You can blind search for her using Noxious Blast.If she attemps to fight you with ultimate active first move away long as you can to make her ultimate less active to increase her strengt.If you arent really skilled enought to find her using Noxious Blast but Orcales Elix.

-Ezreal-Stay behind creeps so Mystic shot harrases them,not you,if he is trying to send ultimate over lane tell your allies about it to prevenet them from dieing or becoming easy targets for other enemies.

-Fiddlesticks-using Noxious blast you can escape drain range,using Petrfying Gaze you can stop it.You should allways stay away from your minions as his Dark Wind or some skill called like that cant bounce on you muliple times.Use Noxious Blast,Miasma,Petrfying Gaze,Flash(Whatever you think its best) to escape his ultimate.

-Galio:Dont let him harras you with his yellow light out of his eyes thing:Choise road that isnt part of his Tornado thingy so he cant easily catch you up.Stun him while hes preforming his ultimate if you arent in it using Petryfing Gaze.

-Gankplank-Use your full range to harras him so he cant Parrley you.Flash out of Cannon thingy.

-Garen-Use Petryfing Gaze,Miasma,Noxious Blast to stay away from him.He is extremely meele champion which cant do anything to you if your atleast 5 steps away from him.

-Gragas-Stay behind most of your team before he uses ultimate.Dont make yourself availible for Body slam.Allways be prepared to suprise him when he uses Body slam over wall.

-Heimdinger-Avoid his granades,make sure you have 3 creeps in front of you to makke yourself less availible to rocket,stay away from his turrets or destroy them using Noxious blast from its full range.

-Irelia-Harras her so she cant farm with Bladesurge and make yourself unavailible to Transiquent Blades.

-Janna-Pay atention where tornado is going and use Noxious blast to be atleast half fast as her is with Zepyhr.

-Jarvan-Flash out of Cataclysm,Pay attention where he is and where his Demancian Standar(Shiny Blue Demancia flag) is so he cant knock you to airbone.

-Jax-Stay back when you see his weapon is shiny.

-Karma-Using Noxious blast and Miasma will make you fast enought and make her slow enought for you to escape Spirit bond.

-Kartus:Once he reaches lvl 6 buy Elix of Fortitude so you can get bonus health when he uses his ultimate(use it if your low and dont want to die by him)

-Kassadin:Try not to make yourself availible to his abilities.

-Katarina-Flash away from her when she uses her ultimate and try to stun her.
And OWN her in lane becouse she took all glory from you :D

-Kayle-Go away from her once you have saw her weapon is full of fire till fire is off.
Dont waste your spells on her since she used her ultimate(When she has big golden shield around her)

-Kennen-Stun him in his ultimate.Stay behind creeps to avoid damage from Shuriken.
When he has his shuuriken in hand shiny stay away from him.

-Kog'Maw-Avoid his ultomate charges,Move out of slowdown area,use noxious blast to stay away from him since he gets his movment buff.

-LeBlanc-Dont let her harras you with silence,Play really care when youre low and she is lvl 6

-LeeSin-Stay behind creeps to make yourself unavailible to Sonic Wave,dont let him knock you,
Dont come to near to him so he cnat slow you down.

-Lux-Pay attention to her position,from where she is make sure that he skillshot can get 2 minions before you.
However if your runnning from her while low and her only chance to kill you is her ultimate dont stand near wall as she may get you in edge of death,try to stay in center and allways be prepared to avoid the light or flash out of it.
(I made that letter animation only for lux becouse other skillshots can hit only 1 dude while Luxes 2)

-Malphire-Make him unavailible to knock you inn air(Dont stay near your teamates in fight)
/(Flash out of range he send himself)

-Malzahar-If he is level 6 be ready to commit with his combo.

-Maokaio-In teamfights stay away from his ultimate area and run from sappings.
When he is charging to you and you are prepared to fight create miasma at place you are and stun him. if he is long enought in miasma you will kill him with twin fangs and ignite.

-Master Yi-Constantly harras him in lane,DONT ALLOW HIM TO FARM!Avoid attacking him while he is meditating.

-Miss Fortune-Move out of her ultimate if you cant reach her and stun her,however your flash should allow you to reach her and stun on time.Use the Luxes type,make sure you have 2 minions before you and make sure you know her position so she cant get you with double up,like with lux.However if she tries to come closer to minion that was 2nd backup for double up "Minion" use your miasma for ennsured ranged harrasment to fade her strut off and unalow her to do so.

-Mordekaiser-He is also very meele champion like garen withoun charge so staying away from him while harrasing will alow you to MAYBE kill him.

-Morgana-Stay out of her gas thing,avoid her bind,and flash away from her when she casts her ultimate.

-Nasus-Stay away from his spirit fire,dont go to close becouse he will slow you down and make you availible for his teamates or his basic attack which deals signifant damage when buffed with his skill.DO...NOT ATTACK HIM WHEN HE USED HIS ULTIMATE YOU JUST GONNA WASTE YOUR MANA AND HE ****ING GONNA BE UNHARMED.

-Nidalee-You are enable to catch her up in cougar form,and there arent many champions that can do it,remember it.Early harrasement while Deadly Cadnece is active will keep you full of mana and force her to use heal or die.Or farm her mana.You gonna have more mana then her if you force her becouse like i previously said you have your Deadly Cadnece.

-Noctume-Be ready to stun him once he charges on you using his ultimate if youre low.If you are ready to fight use miasma at your position

-Nunu-Stun him in his ultimate.

-Olaf-Dont use petrfying gaze on him while he used his ultimate.

-Orianna-Be ready to push on her while ball isnt near her.

-Pantheron-Move out of his attack..dunno its name but it has effects like corkis thing...AH IM LOST :D Sry sry.

-Poppy-Dont allow her to charge you in wal

-Rammus-Make him lose his movement roll buff in minion

-Rekenton-Dont allow him to stun you..

-Rumble-Avoid his harpoon,Stay away from fire thngy.Dont walk over his ultimate area.

-Ryze-Stay away from minions so his spell flux cant bounce on you mltiple times.

-Shaco-Dont brush againist him,Beware from toys.

-Sion-He has epic stun but its short range and you can stay away from it

-Shen-When you think he has ultimate ready dont fight againist his allies in 1v1 if you arent atleast 2miles away from turret or champion or both :D

-Singed-Dont go in his gas area,Dont chase him down if his poision is active

-Sivir-Avoid her boomerangs

-Sona-Dont stay in group with your team so you cant get stunned with them

-Soraka-Stay out of ger Starcall range(Its so ****ing low)

-Swain- If you are going to stun him stun him while he is in raven form,move out of Nevermove.

-Taric- Dont get too close so he cant damage you with his spell that has aura...I dunno how its called i dont play alot gay champs.

-Teemo-Buy Orcales Elix if he goes for AP since his murshroom can significantly damage you.

-Tristna-Make sure she doesnt push you in her turret with her ultimate,If you desided to take heal dont use it while she have ignited you with expliosive shot.Use Maokaio tip when she jumps on you(with miasma)

-Trundle- Move out his stone

-Tryndamere- Keep harrasing him!!!And dont attack him while he has endless rage on.

-Twisted Fate- Stun him if he is trying to escape using his ultimate(Escape or change lane it really doesnt matter)

-Twitch- If he is focusing you buy orcales elix,you can allways blind search him with noxious blast.

-Udyr- Stay away from him while he is in bear-tiger form

-Vayne- Dont let her harras you with condeem.If you do allow her dont stay near walls so she cant stun you and significantly damage you.Use Poppy tip.

-Vladimir- Make sure he attack you before you attack him,
Tip:
Vladimir Cassiopeia:
10000 health 1000health
Vladimir uses Transuftion and damages Cassiopeia but doesnt get healed
Cassipeia uses Noxious blast
Cassiopeia:900health
Vladimir:850health
His Tansfution is on coldown and he cant get himself healed.

-Warwick-Stay behind him to make sure he doesnt use his ultimate on you

-Xin Zhao-Flash away from him stun him and make sure he doesnt get you,After he charges you.
Use Maokaio tip too.

-Yorrick-Im not sure how to fight him he is new and i dont know his tactic and gameplays

-Zilean-Stay away from ally that has his bomb on,If you have bomb on yourself,and while you have bomb active on yourself move from others so they dont get damaged.Change target if you see he used his ultimate

Flash/Petrfying Gaze:Petrfying gaze has small range so with flash she is enable to damage your opponet.
Miasma/NoxiousBlast:Your Miasma can lead your enemies,when enemies are leaded your Noxious Blast hit is more garanteed.
PetrfyingGaze/Miasma/Twin Fang:Stunning your enemies will keep them in miasma for about 2 second allowing you to place around 5 twin fangs.2seconds-1 twin fang pet 0.5. and one by leaving.

I take Miasma and Noxious Blast by level 2.At level 3 i have twin fang with other 2 spells i can keep poision active.Since level 3 i start building Twin Fang,Noxious Blast and taking Petrfying Gaze whenever availible.

If you been at my profile you will see i already have 2 Cassiopeias builds but this 1 is definitivly the best if you ask me.Well sorry for my english typing.I was rushing.
However before leaving this page watch this: http://www.youtube.com/watch?v=-U2bL5-DQsc
Im big fan of LeaugeInFormer and if you guys are planning to play Cassiopeia you should really see how he does it.Skilled dude.