Hello and welcome to my Cassiopeia guide. This is my first guide posted so any constructive criticism would be very helpful and appreciated. I made this guide because with some builds i've seen and tested, none really gave her enough power or mana to function too well.
I have tested this build and find it to be my favorite, and hopefully you'll fidn it useful too]

I don't really know how to put pictures up for these paragraphs, Sorry!

I started with doran's ring because it helps her all around early game with AP and a bit of hp because she is so damn squishy. She will most likely need an hp pot early om because she will be harassed and one hit does a ton of damage early on too her.

I get boots next because she is very slow, and the extra speed early game will help a lot with hitting with your noxious blast.

I get tear next to help her keep mana and build it up for archangels. Archangels is one of the best things for cass IMO because she spams abilities frequently and that'll build her up some mana and AP.

I start building RoA next because it helps her with survivability and more with mana.

I get rylai's next because it is very helpful for her. If you hit someone with noxious blast, itll be easier to finish them with more noxious blasts, it'll help her slow more with miasma and her ult, and it helps to harrass with the short range of twin fang.

Rabadons. Amazing ap to help her do tons of damage. Thats about it.

Sometimes ill get a spell vamp item like will of the ancients for matches taht i get harrassed frequently and need to heal without leaving my lane. Cass is really good will spell vamp items because she can farm very well to regain hp.

You could also consider getting the new hourglass item for defense if needed.

I choose to max noxious blast beacause if you continually get it on the enemy champ, you will do a lot of damage and will last hit well if you lay it down well enough.

I max miasma next because it is very helpful for doing light but annoying damagein team fights, and it slows which is very helpful as well. Also, miasma does damage as soon as its laid, so if you get good enough timing you can finish them by laying down miasma at the last second.

I get twin fangs last because to be honest, it has too short of a range and doesn't have good enough scaling to really do high damage. Her poisons are better IMO.

I get basic AP ruens for quints and glyphs, and mana regen for seals and magic pen for marks. With decent mana pen her poisons can eat away at magic resist tanks, like galio (His passive gives him more magic resist right?)

Good:
Ignite- Pairs well with her poison to last hit
Flash- Good escapse and if you are able to do it, you can flash forward and hit them with a noxious blast to finish people if needed.
Ghost- Escape and finishing, just like flash.
Cleanse- Shes squishy, and getting out of stuns or slows may just be enough to save you.
Clarity- She is mana hungry, so clarity can be helpful.
Bad-
Teleport- I just don't like the spell really, but if you want you can get it
Clairvoyance- Once again i just think that cass doesnt need it but if you are good with it by all means take it.
Rally- Shes a caster. Nuff said
Revive- I don't need to really explain why right?
Heal- She will probably die after you use heal anyway if you really need to use it.
Fortify- Doesn't need it. Let a tank use it.
Smite- Doesn't jungle early on and farms so well late game she doesnt need it.
Exhaust- IMO she already will slow enough with her abilities and her rylai, and now that it just reduces damage, not blind, that she doesnt need it even to save herself really.