Cass is one of my favourite champions.
Heres quick guide on how to play/build her.
Cassiopeia has some of the best sustain damage of any caster. Her Q does a crazy amount per tick (even at lvl1), boosts speed by 25%, her E is such an amazing complementary skill, normally has a 4 second cooldown, but if it hits a poisoned target (e.g from her Q or W) its cooldown is reset to 0.5 seconds. Her W is a good slow, but only use it for the slow or that little extra farming, I generally don't level it till lvl 13, since its shitty damage. And oh god her R, one of the best anti tower diving tools you'll ever see. the arc covers the entire lane, stuns for 2 seconds (if they're facing you) or slows if facing away from you and does 200 damage (0.6 AP ratio). This works really really well with Flash, nothing quite like a flash + R, confuses the fuck outta someone and allows you to land some sweet deeps. Not to mention her passive, 10% less mana cost on her spells per spell used, stacks 5 times. Basically, at 5 stacks, you DOUBLE her mana pool. This includes her ult, which sits at a tasy 60 mana at lvl 1 at 5 stacks.
I'll assume I've only got my runes and Dorans Ring at 39 AP
At level 2, her Q does 95 damage(+21)(0.55 AP ratio), now, at 0.5second cooldown thats well over 220 DPS, AT LEVEL 4. AT FUCKING LEVEL 4. Her Q does 115 (+36) (0.9 AP ratio) at lvl 2. So, in one second, you've done (potentially) 260 damage. And my god, do they notice it that early on.
My general playstyle with her is SUPER AGRESSIVE. You get nothing done letting your lane push, even if they have a jungle, you can escape without flash using just your Q early game. Udyr's useless ganks can't get close, it negates GPs slows quite nicely etc. etc. Use flash if you really have to, but make them pay, throw down a Q and E him a few times. Don't level your W at all, its useless and stops you from doing stupid amounts of damage early game. The slow is tempting, but since you have a speed up on your Q
A skill you _have_ to learn though, is where and how to land your Qs, this is your bread and butter skill. If you can't land it, you can't do anything with your E. I probably should put a few pictures up explaining this, but because of time constraints I won't right now.
How I tend to engage, is I either take solo mid, or go jungling (yes jungle), You have to push them to their tower. Make the scared of you. Constantly harrass with your Q, every time you land it, follow it up with an E. Keep them in a constant state of fear, only way to work.
I prefer to take flash and teleport. Flash for the scary tower dives, and teleport for the "OMG A CASS JUST CAME UP BEHIND US AND RAEPED US GOOD" moment. Take wards, I like to pretend they're like save points if my teleport is up. Low on health? Hmm I'll just save here *places ward*, recalls, teleport back, full health *BOOM DEAD KARTHUS OR W/E*.
Edit: Forgot to add my build order.
Normal Cass. Dorans ring (Health, for getting in real close and E'ing like a bitch, plus mana regen, plus AP is bestest) > try to go back with enough for anothers DR, and lvl 1 boots, (that extra health is so useful for dodging ganks and everything. The mana regen + what ever your runes are will sustain you pretty much indefinately in lane if you don't spam skills) > Sorc shoes > Hextech revolver > TotG (Q and E'ing alot, so why not make it worth it) > Rapeadons (Games are usually over by this point) > AAS > Will of the ancients > (then what ever, really if you're at this stage you've done something wrong or your entire team sucks).
I'll have to post a replay of me playing it. Its like poetry or something.