Sivir has just been changed and i dont see much of new changes in builds so i would like to share my build and see if there is any tweeks that should be done.

I go for a early attack damage build, this makes me excell in early game lane, gives me dominance and makes the farm go easyer. for the rest armor seals, flat mres glyphs.

For mastrys ofcourse a full offense build with some extra manaregen for sustain. Dont forget to take the Magic pen mastry!

Dorans blade or Boots depending on what support i have with/without healing
After that i try getting some sustain with 1-2 dorans blades and complete my boots
Now if you feel like goin for a manamune you need to start thinking about getting that tear, its not expensive and gives you nice mana to harass your opponent.
Once you got this tear you can start stacking it and you can eigher complete the manamune or go for bloodthirster first.
After completen both items i prefer getting somekind of a health item like Frozen mallet/warmogs,..
Here after you can either start building more of a crit build(most recommended is atmogs and infinity edge or if you took frozen mallet you can stack bloodthirsters, get blackcleaver,..)
Now if you feel like that aint enough attackspeed phantom dancer could also be in place somewhere

You start off by getting all 3 spells, after you start maxing your Q spell to make early harass possible.
in between you want to either start leveling your E or W depending on what kind of opponent team you have, much or not much cc.. If you encounter not much cc i recommend goin for W

I run wiht a general Flash exhaust combo, exhaust can be replaced by cleans( overkill is never underrated against massive cc teams)
Another option is to run ghost for your movability since you are a verry slow champion! and you want to keep up with the chase even without your ultimate!

when a fight is about to start or is already started go straight for your ultimate, your ultimate is the strongest buff in game! try to stay in the back of your team at all times and position your Q soo you hit as many targets up and forth. if you need to move forward to get to a enemy carry activate your shieldspell in time! that is a spell that can make you win or loose the teamfight!

once mid game you should be able to farm waves pretty easy with Q and W, just throuw your Q trough all the minions followed by a W ! Farming is the MOST importand aspect of sivir! YOur items ARE EXPENSIVE! if you can keep this up you will dominate lategame together with your team!