Sivir's top two qualities is her built in movement, and her ability to completely shred through a lane of minions and enemies. With the mixture of her aoe skill shot and multi hit utility attack, in my opinion places her as the number one choice for a high chance early lane domination or holding. She can maneuver well while putting out a nice poke, block return pokes, and clear out the farm while keeping the enemies held back.

Most adc characters are built around mostly attack speed, crit and life steal. With this item build we will try and hone in on her kit, maximizing her offensive utility spell ricochet while adding quite a punch to her skill shot boomerang blade. Sivir's main focus is her mobility and aoe damage output. Her aoe ricochet is amazing for farming, clearing waves, and keeping enemies backed away from objectives and forcing them to play cautiously. So instead of heavily relying on attack speed like most adcs, we are going to let ricochet carry us.

For starting off the game i would grab a faerie charm and health pots, or just mana pots and health pots. This way you can keep the fuel you need to keep that ricochet going, and in case of early game aggressiveness, you will be able to heal damage sustained and keep mana for a spell shield if needed. Once the gold starts becoming available, the first item i would build into would be Spirit of the Elder Lizzard. Its boost in ad isn't very high, but it offers a small portion of health regen, mana regen, cool down and a nice passive that will prevent your jungler from offering up the red buff, and the exp and gold that comes from killing the buff minion. This items passive is also very handy at helping to clear minions and keep damage applied to the enemy champs, causing them to burn through pots and resourceful skills.

The next item i would try and grab would either be a completed pair of boots, or grab basic boots,vampiric scepter and start on last whisper, all depending on the situation at hand. Sivirs passive gives her a nice little speed boost every time she hits an enemy champion, helping her either catch up, make a quick turn and run, or just keeping her light on her feet to dodge in coming pokes when landing a poke on the enemy. I have listed three boots, all three very nice on sivir, and all three would go according to how you play, or what would be better needed. If you feel like you need a better attack speed boost, then grab the berserker's. If you feel like you could use extra speed, grab the bots of swiftness. Or, if everything is going just fine over all, then grab the Ionian boots of lucidity for that extra cool down so you can keep those skills going. Either way, once the boots have been purchased, the best thing you could do is buy the boot enchantment furor. This will give sivir a movement speed boost for every hit on an enemy champion, just like her passive, causing her basic attacks or skill hits on the enemy to grant her more mobility and make her twice as deadly.

After the boots and last whisper, i would build either the black cleaver, or Blade of the Ruined King. If you cant seem to keep yourself alive long enough to deal the killing blows, then Botrk would be your best shot. The scaling damage based off of the enemies hp is wonderful, but healing factor will help you sustain in the fights ahead. With black cleaver, you will gain more cool down allowing for faster use of skills, a small boost to health which is always nice for ranged characters, a decent boost in damage and every hit will decrease the enemies armor, stacking with your last whisper to just further allow your damage to seep through.

The last and final item i leave as an open choice. You could either grab a Blood Thirster for extra damage, and extra sustain in fights,or you could grab one for the following for utility reasons;
Runans Hurricane: A high boost in attack speed, a passive that adds more damage to basic attacks when fighting a group, and more wave clear.
Static Shiv: A nice boost in attack speed, a decent boost to move speed, a small crit chance boost, and additional damage from passive that will add more damage to basic attacks in one on one fights as well as team fights, and also adds more wave clear.
Frost-born Gauntlets: A small boost in ap(not really a needed or wanted boost, but it still will add a very small amount of damage to your boomerang blade), a good boost to mana which will help insure more skill usage when needed, a good boost in armor which will help when bruisers, fighters, assassins, and ad tanks close the distance as well as help with return fire from adcs, and an awesome passive that grants skill based champs a bonus in damage after using a spell and makes this extra damage an aoe slow as well, giving more utility to sivir and team mates as well as more aoe dmg/wave clear.
Frozen mallet: A tiny boost in damage, a great boost in health, and a passive that will reduce movement speeds of enemies hit, from minions to champs, giving sivir and her team an advantage.

With runes, it is really up to the player. I prefer to use movement speed quints, and attack speed everything else. It may seem crazy to use nothing but attack speed runes, but with the item build above mainly focusing on utility and up front damage instead of attack speed, the attack sped runes will come in mighty handy. The movement speed quints will give sivir a great edge early on in game, helping her to run forward and poke as well as dodge incoming pokes and ganks. Also, being able to constantly move around quickly while clearing and pushing will keep the enemies on edge and worried.

With the masteries i will say the same as i did above with the runes, it is up to the player, but i feel like with these masteries they will support almost every item in the build as well as all of sivir's kit.

In my eyes sivir is a champion that was built so that every part of her kit would be built around and used, allowing her skills to carry the player forward. With almost every champion i play and sivir not being exempt from this rule, i put one point in the best skill/most important skill for the build first, then one point in the second important skill, following up with the last skill for level three(not implying spell shield is not important for this build, i just think it can wait until level three to be unlocked, and once unlocked does not really need to be leveled until later in the game).

With all three skills by level three,you have a wider variety of plays that can be done. After level three, i would max out ricochet first and for most, followed by boomerang blade and then spell shield(and of course put a skill point into her ult every time you have the chance=self explanatory). This way or ability to farm and clear waves is maxed out early on when its most important, and her ability to dish out damage while pushing enemies back can be utilized quickly and efficiently.

As far as plays go, it think its fairly simple to grasp, just instead of the traditional walk up poke back off, i would walk towards the enemy, then veer from side to side, keeping myself constantly moving. Once you feel like you can use ricochet on a minion and hit hit the enemy champs as well as the whole group or at least majority of the group of minions, then you should do it. Once the enemies are trying to out dodge the ricochet(which i find quite amusing) you can then normally get a clear shot on them with your q to dish out some heavier damage.

You don't have to reserve your ricochet only for champ hits, its good to use it often enough to keep the minions back and keep gold in your skirt pocket, but i would save your q as much as possible unless in a combo attack with your ricochet. Your q uses quite a bit of mana, and has a not so terrible cool down time, but if used un wisely can leave you in a situation where your enemies have more damage on the ready then you do. Your best bet for early game play would be to stay safe as possible, but to still be aggressive. A better way of saying it would be simply to say be passive-aggressive. Try to keep your enemies back and get in good jabs while you can, but not at the risk of harming you or your ally. Patience and good timing wins more games than you think.

Before i sum this all up, i would first like to apologize for any bad grammar and such, i am extremely tired but cannot sleep, and this key board hates me. I would also like to apologize for the over all simplicity and lack of depth my guide may have, as well as any rambling or repeating i may have done.

So the summary for sivir build is to utilize her kit, her spells, her everything. She was ade to be a wave clearing, aoe, group destroying monster of an adc. Crit damage and insane amounts of attack speed is nice and has worked time and time again for almost every adc as well as any ad characters and sometimes just for giggles its even been done on ap champs. But to me, sivir was not meant to be that kind of champ. She was meant to hold that early game lane safely, and if possible force them back as far as you can, and even destroy that tower before the ten minute mark(which i have done and seen been done with sivir, from the very first sivir to the current version we have now)and instead of that one on one combat based builds that go with pretty much every adc,this one in particular is a team player all the way. She was meant to stand in the back, behind the bulk of her team, and devastate the whole enemy team, all at once.

If you find my guide neat or helpful, i would like to say thank you for your optimism and i hope it serves some one well. I do not mind friendly criticism at all, but i will ask people kindly to refrain from rude remarks.

P.S. For a lane mate, i would chose a tanky champ with decent utility foremost, a good choice would be leona, maokai or malphite. If not, i think the second best would be a nami or sona for the heals and boost in movement speed.