Arcane Supergirl is currently my favorite blaster because if you play her right you can dominate an entire teamfight. 

Spells~

Q-Breath of Rao- This is AS' main spell, I like to take it level on ebecause the damage is pretty strong for a level one spell, espcially if you can it on multiple enemies. In the late game, use this spell to harrass your enemies before a team fight, and then to burst/zone them in the team fight, sometimes just seeing the fireball late game will send an enemy running! This skill is also your best farming tool. A level 4 BoR+Firewall can nearly completly kill a wave of minions.

E-Pyrolyze- This is AS' only form of hard CC. Use it to harrass enemies in lane and to escape from ganks. Late game make sure to send it through your Firewall to get the better stun, it could give you valuble time to get your full combo on the person! 

W-Firewall- This is a very important skill to know how to use. If either Breath of Rao or Pyrolyze go through the wall, they get a buff. BoR gets more damage and Pyrolyze gets a longer stun. Remember if either of these spells go through the wall, the walls cooldown gets reduced. The wall also prevides amazing zoning in teamfights, use it to block your enemies andvance and to send your spells through it.

R-Rao's Wrath- This is probably my favorite ultamate in the game next to SS ult. Once casted the firest time, you get 2 other casts before it goes on cooldown. These blasts are extremely long range and if hit, can do massive amounts of damage. Use to burst an enemy from full to nothing with your other spells.

Passive-Daughter of Rao- Not going to lie, when AS was first announced, I hated the idea of this passive. But after playing her, I like it. You can use it to harrass after using a spell, you can use it to add more damage after a combo. This is a very versatile passive.

Combo~

Your main combo to burst somebody from full to nothing will be, W,E,Q,R,R,R (If you want to be really pro looking, you can try and use your E first then the W as the E is flying towards the enemy). This combo can kill most champions if you hit the E (Don't try this on Enforcers, they could probably live). If you miss the E, they can dodge the rest of your combo so you shouldn't continue if you miss it.

The combo is the same if you want to just harrass an enemy. Just leave out the ult, you may need that later.

Items~

Start
When you start you want to buy Nil Ring and teir 2 health vial and teir 1 will vial. If your playing on Coast City you can also buy either teir one Doctor Destiniy's Dreamstone or teir one The Logoz. On Gotham Heights you can skip the Nil Ring and vials and go straight into you core build. You should also skip The Logoz because its not worth the money to have to stack it on heights. Your first main buy on either Coast City or Gotham Divided should be to at least get teir 2 The Logoz, and if you have the cash get teir 2 DDD.

Core
You want to go immdietly into your Cosmic Staff, the 2  passives and the CD reduction and power damage make it an essential item. As soon as your Staff is done you want to buy your Starheart. After this you should get a Nerons Contract for the stasis, if used correctly you can avoid a lot of damage. If you are doing really well, you can buy Fatality's Energy Lance. If the enemy team is building Power Armor, you can buy The Book of Eternity for Power Penetration.

Late Game
Late game items is just finishing DDD and if you are getting focused sell your The Logoz for either Ra's al Ghul's Robe, Helm of Fate or Atlantean Royal Seal.