So simply put, I decided to come back to Sivir, one of my first champions, and still, my favorite ranged attack damage champion. I quickly looked through quite a few builds around the web, for her, but found that there were a few things I felt I wanted to change for my own build. I found these minor changes to be very highly effective, if properly utilized, and as such, a guide became an obvious outlet for my own venting, and your enjoyment.

Pros:
*Great early and mid game damage
*Good end game damage
*Good farmer
*Decent survivor w/ult, dodge, and shield
*Great lane/tower pusher
*Great backdoor champion
*Great team steroid with ult
*Great end game multi target dps

Cons:
*Squishy
*No natural CC
*Not the best end game single target dps
*Runs low on mana quite often

Fleet of Foot applies a passive dodge to Sivir, as long as she's moving. Because of this, taking steps between shots becomes highly effective, negating upwards of a quarter of incoming damage, both from minions, and attack damage champions.

Boomerang Blade is the bread and butter of Sivir's harassment and spike damage. It's a tricky skill-shot to get the hang of, but is very versatile, presenting incredible single target and multi-target damage. I max this first as it does absurd damage in the early and mid game. It enables you to zone your opponents more easily, and if they overextend, it will net you kills.

Ricochet is Sivir's mid/late game farming and pushing skill. It clears creep waves incredibly fast, and is a very good single and multi-target poke, as your shots can ricochet off a creep wave and hit opponents who are nowhere close to you. However, it does consume quite a bit of mana over time, and can cause turrets to target you if your shots bounce to an enemy champion. I advise toggling this skill off when targeting turrets with champions nearby.

Spell Shield is Sivir's survival utility skill. I get a point with it early on, but no more than that, because while a well timed shield will save your life from an incoming stun or killing blow, it's not often that you'll face threats of that nature frequently enough to justify more points into the skill at earlier levels. This is a skill that takes both some reflexive practice, and knowledge of the champions you're up against, but when used properly, it will frequently save your life.

On the Hunt is an incredible ultimate. It can allow you to bash down towers very quickly, take down enemy champions, chase, escape, and best of all, buff your entire team, which can definitely turn team fights in your favor, very quickly. It gives you and surrounding allies a movement speed and attack speed buff.

Sivir is a master of back dooring. I take Teleport because Sivir is at her best when she's doing one of two things, split pushing (or back dooring), or tossing blades around in the middle of a team fight. Teleport enables Sivir to bounce back and forth between points on the map, putting her in position to do a split push, or to quickly join an imminent team fight. It also allows her to farm full time in the early game, which is always beneficial.

Flash is stupidly good. It allows for absurd escapes, as well as instant repositioning to land a finishing Boomerang Blade on a low health opponent. I take Flash on just about every champion I play.

Other viable options:

Sivir Does not rely heavily on spells to escape. Her skills provide a lot of the utility she needs in most situations, and as such, Clairvoyance could be a possible pick, if no one on your team is running it.

If you're having issues with people escaping with a stupidly small amount of health left, Ignite could be what you're looking for. Not only is it a good finishing move, it also helps deal with champions who you can't seem to phase, due to healing. It serves no further utility, however, and as such, it's not ideal, in my opinion.

The Opening:

Philosopher's Stone
There are two ways I like to open with this build. The first: Pick up a Doran's Blade. I'll do this if i'm expecting a highly aggressive early game. The second: A Regrowth Pendant rushed to a Philosopher's Stone and an optional potion. If i'm expecting more of a passive lane, I'll go with this opening. I've been favoring the second opening a lot lately, as the added mana and gold income really pushes a mid game advantage.

I'll follow both openings up with Boots and almost always Berserker's Greaves as they are a very cost effective DPS buff, and Sivir often has enough natural counter-gank/cc to need early tenacity.

Following this, I'll grab an Avarice Blade for more gold income, and the added critical strike chance, and if I have the gold, a Vampiric Scepter for added sustain.


Philosopher's Stone

Mid game:

I mark the opening of Sivir's mid game with the purchase of her Bilgewater Cutlass. The lifesteal allows you to heal up quickly after fights, by farming lane, and the added damage helps make you a bit more of a threat, but most notable, the active acts in place of an Exhaust, in that it allows you to focus down a lot of champions much more quickly, and pick people off who are out of place in potential developing team fights. It also provides with some extra escape utility. I follow this up with Guinsoo's Rageblade as it turns Sivir into an auto-attacking monster, and provides her Boomerange Blade with a very scary damage spike.


Philosopher's Stone

End game:

At this points, our items have Sivir's momentum up. her damage is decent, her survivability isn't terrible, and her lane pressure is pretty awesome. We have a few options now, though my favorite by far, revolves around boosting damage and critical strike chance, as well as solidifying what the build already has going for this. I first, build towards an Infinity Edge, for the excellent damage boost, and absurd critical strike damage. In order to keep her Boomerang Blade damage as frightening as possible, I follow this up by completing my Hextech Gunblade. Now, depending on what opening I went with, and what I feel I need first, I'll complete my build with a Phantom Dancer, and Youmuu's Ghostblade, in either order. Youmuu's Ghostblade is exceptionally nice on Sivir, as it acts in similar fashion to her ultimate, but it's a personal buff, only. I use it for back dooring, 1v1 fights and chasing, and essentially anywhere, escaping aside, when I would otherwise burn my ultimate, but team mates aren't around to benefit from it.




Situational Items:
Now, situationally, I may forgo some or all of the items I have down as end-game items, in favor of other more effective replacements.

Offensive Items:

Black Cleaver: If you want to back door faster, and still be very effective against squishy targets, without relying on critical strikes for the majority of your damage buying one of these can be a great go-to.


Bloodthirster: If i'm getting poked an absurd amount, and it's keeping me out of fights, I'll pick one of these up for the added damage and life steal. It also makes you very difficult to finish off, when fighting near a minion line, as you'll heal life from all the Ricochet damage as well.


Last Whisper: It's not the most effective item on Sivir, but it becomes almost necessary if the opposing team decides to stack armor.

Defensive items:

Thornmail: If you're getting smacked around by their AD carry, this is an inexpensive quick fix.


Randuin's Omen: For more general survivability than Thornmail, but still favoring armor.


Force of Nature: Pick this up if you're facing lots of heavy magic damage champions.


Banshee's Veil: If CC is a large threat, and Spell Shield isn't covering all your needs, grab one of these. It's also a strong magic counter.

Hybrid Items:

Warmog's Armor and Atma's Impaler: The combination of the two of these will give you some excellent general survivability, while boosting your base damage output, considerably.


Frozen Mallet: Sivir has no natural CC, and this build's only CC is provided by the Hextech Gunblade's active ability. If this isn't proving to be enough CC for your time, pick up a Frozen Mallet. It will provide a minor slow to anyone you target, and boost your damage and health a bit.


Wit's End: This is one of my favorite items in the game, and while it isn't excessively effective on Sivir, it still does it's job. Pick this up to hybridize your damage a bit, with some magic damage, as well as provide a nice buff to your magic resistance. Oh, and some attack speed as well. Always good.

Greater Mark of Desolation: This Sivir build provides a lot of attack speed, damage, and critical strike damage. Armor Penetration is basically the only worthwhile thing left, in boosting Sivir's damage.

Greater Seal of Replenishment: I use these because they provide Sivir with enough mana over the game to be consistently threatening to the opponents.

Greater Glyph of Magic Resist: As a ranged AD champion, Sivir's largest weakness is magic damage spikes. I take these to compensate for some of this threat.

Greater Quintessence of Desolation: I take these for the same reason as my marks.
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I'm currently testing the viability of other Seals, especially on the second build, as Philosopher's Stone will provide most of the mana you'll need through a large portion of the game. As suggested by Levidica, I may end up mixing a Greater Seal of Scaling Mana Regeneration set, or perhaps a partial set.

I spec Sivir 21/0/9 out of preference, only. I'll briefly summarize the key masteries that I can see viability for.
Offense:

Deadliness is a good option as Critical strikes are very powerful on Sivir.

This is an incredibly good mastery. The 15% spell penetration will really boost the output of Sivir's Boomerang Blade.

I do consider this mastery viable for Sivir, as it does help her last hit in the early game, and in the later game, in conjunction with Ricochet, speeds up her creep wave pushing.

Lethality is a potent mastery on Sivir, if you decided to build her at least partially for critical strikes. they add an extra 10% to critical strike damage, and as I said before, Sivir likes her crits.

Defense:

Combined with Sivir's passive, Nimbleness will be procing very frequently whenever she's in combat, chasing through creep waves, or escaping.

Sivir does not have a lot of health. Veteran's Scars will help her get through the early game via compensating for this.

Ardor is an excellent mastery, if you feel like specing all the way down to it. It adds a very nice attack speed bonus, and a slightly less useful, but still nice ability power buff.

Utility:

A good mastery for Sivir. It allows for a slightly further edge in her mobility, and lane pushing capabilities.

Awareness is excellent on Sivir. It helps her gain an early and mid game advantage simply by having superior stats to the opposing team due to extra experience.

And if we still don't have teleport up enough for our liking, Presence of the Master will surely assist this predicament.

Now I briefly mentioned a few of these points above, but for clarity, i'll cover them again.

Early Game:
Sivir's early game is all about last hitting. Her attack animation takes some getting used to, but it's quite effective once you get it down. Don't waste your mana in the early game. Use your Boomerang Blade when your mana is full, to harass, or to push a creep wave/last hit multiple low health creep. Never waste your mana unless you're about to return to base, or unless it will net your team a kill. Position yourself, if you can, so that your blade hits the enemy champion twice, without hitting any minions beforehand, for maximized damage. And once again, prioritize last hitting creeps over harassing.

Mid / End Game:
Now, you can really start pushing lanes make sure you have wards up before pushing too heavily, or at least have vision/knowledge of the location of most or all of their team. Farming in this stage, will come somewhat naturally. Push lanes, and if a team fight seems imminent, don't hesitate to run over and join in. Your damage and ultimate will be very helpful in team fights. whenever there's a break in the action, either continue farming, or return to buy items. A good tactic at this point is to push one lane heavily, and then back off, and Teleport to the far opposing lane and quickly knock it's tower down. You can also split push quite easily, and sometimes, it's wise for the majority of your team to bait the opposing team at either baron, or the opposing lane, while you push bottom, or a separate lane on your own. this forces the opposing team to either team fight under your team's terms and lose a tower, attempt to kill you and lose a tower or baron, or split themselves, and risk an uncoordinated team fight, and a very difficult tower defense. Similar tactics work for pushing inhibitors as well, and by this time, the game's usually more or less decided.

September 10, 2011: Guide published
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It's in a very rough form right now. I just wanted to get the idea out there, as I haven't seen any other Sivir guides quite like this. I'll hopefully pretty it up a bit, down the line here.

Feel free to leave my any commentary, suggestions, ideas, or edits, as well as any questions you may have. I'm more than happy to hear any feedback you may have.