Not Updated For Current Season
Sivir is an squishy character with some defensive spells. She is good pushing turrets as core, so any build is good for her at that task and it is not an issue to discuss what build is good for that. She can do insane damage if she is well played.
Runes of this Sivir are specialized for Boomerang Blade giving 14 magic Pen and 45 AP. Mpen are flat runes which are always useful and AP are cap runes so you will get stronger how more leveled you are. Your damage ability is Q ( Boomerang blade), you can constantly hitting with autoattacks for helping but Q will do the most. Q is based on Attack damage and AP. Attack damage increases always per level on any character. AP increases if you have picked it in masteries or runes, so even initiating with AP items, you will get more damage than AP until lategame. full damage should be 1500-2000 to squishy classes.
Masteries are specced for damage. In utility you only will get more exp, run speed and more gold. The rest of points will be for damage, increasing AP, attack speed, critical, % MPen, CDred etc. All for doing damage.
Items starts with Doran ring's or Spellbook, first if you mid and second if you lane. the you will go to sorcerers boots to rape enemies soon. Hextech gunblade will be the next speccing Boomerang. Then you will get Bilgewater cutlass for Hextech gunblade. You will get spell vamp and life steal from spells and ricochet. just 20% and 20% more in complete than Bloodthirster, and just a little less ricochet damage, while you will get the most damaging item for Boomerang besides external factors as charges or mana/AP dependants. Slow is just a kill machine. Next item is Guinsoo, it gives you Attack speed and a very good AP portion. Now you are a full character.
Void Staff has 2 functions, First of all is adding damage to Q and the other one is doing madred very effective ( Since Madre damage is magic)
Madred is specially good vs tanks it adds a little part of damage to Q and W too.
Malady adds attack speed and lowers resistance. good final item.
Order is RQEW. Ricochet for the end for fast pushing and teamfights. Pushing in lanes or mid can be solo done with Q.
Ghost and Clarity, you are a machine mana expender and you need mana and mana even with spellshield.