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Foreword

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Hello, and welcome to my Sivir build. You may notice that the item build is pretty standard on Sivir, but I put 5 items that you can change out to find what suits you best if you don't like what I put up top. This build will cover Abilities, Summoner Spells, Pros & Cons, items, and early, mid, and late game. Please rate and leave comments, all comments and criticism are accepted.

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Summoner Spells

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My Recommended Spells:
This spell can save teammates, secure a kill, or even save you. This will help you achieve your kills until you get your ult, and even then, it's still a great spell to have.
This is an important spell to have, considering the fact that Sivir is one of the better pushers in the game. This helps you keep your lane control and can save a tower or even an ally in trouble. Great for Sivir.

Optional Spells:
This spell goes great on any champion, and Sivir is no exception. This spell can check for ganks, set them up, and even allow your team to steal Baron if the enemy is trying to get it.
Sivir has some mana issues early if you are trying to harass and farm with Boomerang Blade. when you are out of mana, the enemy can easily kill you early game, and clarity can save you. Feel free to take it.
Your ult can't just let you straight up GTFO like Master Yi's, so getting disabled while running is still a threat. Cleanse can make the difference between you dying or escaping.
Great to set up a gank, catch a runner, successfully tower-dive, or it can save your life. Just a useful spell to have.
Sivir is a pretty squishy champion early, mid, and late game, so getting focused or ganked is a constant threat. Heal can save you in a teamfight, gank, or a tower-dive. It also gives you more lane time early game.
Early game this spell is the cause of a majority of the first-bloods. If you can't chase them, ignite will handle that.

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Spells I Don't Recommend

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While it can be a good spell, I like to leave this to tanks and supports, you need spells for killing and pushing.
As effective as this spell is, you have an ult for chasing and Phantom Dancer will bost your move speed even further. I suppose if you REALLY want it then that's fine, but I don't like it on Sivir.
I think Revive is a great spell when you are new to the game, but try to avoid it because most people call it a noob spell, also I think that as long as you play smart, you will be fine without it.
Since this is not a jungling build, pretty much useless.

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Pros & Cons

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Pros:
-Great pusher
-Devastatingly high damage late game
-Good move speed
-Ult is an aura
-Amazing farmer

Cons:
-Squishy
-Low mana early game
-Often focused in teamfights
NOTE: If you want Sivir to have a little bit more survivability, you can follow a 21/9/0 mastery build, and take flat health quintessences.

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Abilities

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Sivir has an increased dodge chance by 10 / 15 / 20 / 25% while moving. The Dodge increases at levels 6/11/16.

Great passive, making it easier to escape, especially if you threw in Ninja Tabi.

Sivir hurls her crossblade like a boomerang, dealing magic damage to the first unit and 10% reduced damage to each subsequent target.
Cooldown: 9 sec
Cost: 80 / 90 / 100 / 110 / 120 Mana
Magic Damage: 20 / 70 / 120 / 170 / 220 (+0.75 per Ability Power)(+0.75 per Attack Damage)

Your main harass and a huge nuke later on. This ability will drain you mana fast if not used carefully early on, but thats where Tear of the Goddess comes in. This will get your farm, charge your Bloodthirster, and make tower-humpers cry. Great spell overall.

Sivir's basic attacks will bounce to additional target(s), dealing 22% less damage with each bounce (only the first hit procs item effects).
Cost: 6 Mana per attack
Bounces: 1 / 2 / 3 / 4 / 5

This spell will help with your farm greatly, and when combined with Boomerang Blade, it will deal serious damage to groups of enemies that are grouped up. Try to keep this on whenever possible.

Creates a magical barrier which blocks a single enemy ability used on Sivir. Lasts up to 3 seconds. If an ability is blocked by the shield, Sivir regains 150 mana.
Cost: 75 Mana
Cooldown: 22 / 19 / 16 / 13 / 10 seconds

This spell is grabbed at level 3 because that's when casters spells start to hurt a little more early on. It is left until then because you shouldn't be taking the hits anyway, that's what tanks are for. If you do end up taking a lot of spell damage, pick up another level or two so the cooldown is reduced.

Grants Sivir and nearby allies 25% extra movement speed and a percentage of attack speed (a third for her allies) for 15 seconds.
Cooldown: 90 sec
Cost: 100 Mana
Area of Effect: 1,200
Attack Speed: 30% / 60% / 90%

Your ultimate, and the spell that will most likely secure most of your kills. Also a great chasing/escaping mechanism (Not as good as Master Yi's). Plus the added aura effect and your team will tear things apart (hopefully).

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Items

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Gives you a nice beginning mana boost, considering the fact that your main harass takes quite a bit of mana, this is nice to have.
Pretty obvious why you would want these. Great for early game and should be gotten on every champion.
These are great due to attack speed, but can very easily be replaced with basically any boots.
gives you nice mana and mana regen while giving you that very nice passive. once your mana problems are solved, feel free to replace this with an item of your choice.
The lifesteal is great and the passive is very nice, bringing you up to 25% lifesteal and 100 damage.
The attack speed, dodge chance, and move speed are all great on Sivir.
I've had games where the enemies will have basically all weak champs and I'll get a Madred's and be asked why I did so? I can't understand why some people can't realize that if it works good on tanks, it will work amazing on weaker enemies.
Now this item is completely situational. If they have a lot of armor or multiple tanks, get it. If not, get something more useful such as a Frozen Mallet.

Possible Items:
The slow just requires you to catch up to your enemy with your ult and let your auto-attacks do the rest.
The 40 armor penetration is the main reason for this, even though the added stats are nice.
Attack speed, move speed, the effects of Sheen, just a great item.
Cranks up your crit damage and gives you a nice 75 damage, very nice item.
If you maxed your Tear of the Goddess passive then this can be an effective item.

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Early Game

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Before the game starts it is important for all Sivir players to decide, do you want mid? While mid is great for Sivir, laning can be just as effective. Once your choice is made, go to your lane and start by last-hitting and harassing if needed until you get Tear of the Goddess. Once you have this, you can farm/harass with your Boomerang Blade without fear of mana, because the more you lose, the more you gain (If that makes sense).
For those who went mid, once you feel like you have a nice farm, continue to farm, but gank whenever you want some extra cash, a lane needs help, or the enemy is so bad that it's pure fun to do.

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Mid Game

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Now the team ganks start and the enemy team (and hopefully your team as well) are grouping up and ganking. This is where Sivir starts to really notice her damage, as the enemies are close to each other, big mistake when there is a Sivir. Just Boomerang Blade, activate Ricochet, activate your ult, and watch as you and your teammate either:
1. Rip them apart.
2.Scare them off.

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Late Game

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Now that teamfights are happening all the time, your Boomerang Blade gets to do even more work. Once a teamfight starts, always hope you don't get focused, it usually won't end good. Once your tank has initiated, just Boomerang Blade when it's available, ALWAYS keep Ricochet on, and make sure you use your ult, it can change the tides of a fight. Hopefully by the time late game started you had a majority of your build complete, and if you did and played smart and stuck together, you had a positive K/D/A and had a good game.

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Afterword

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I hope that you rate this build, leave some feedback, and had success using it like I do.