This is my first build.
so pleas do comment.

the items in this list should support your spels and thanks to the cooldown you should be abail to pop your ulti reguler to be a great support for your team.

When should you use this build and when not. because sivir is a character that easily die's. You end op feeding the opponent sometime's. But even whit a few deaths your support end-game will make up for it. Because the game isn't how gets the most kills but: 1) Forcing your opponent to surrender, or 2) Destroy the enemy nexus. So if you have a burst of energy to destroy Turret after Turret, and the inhibitor. Too gain exes to there base and eventually destroy there nexus even whiteout any kill and huge deaths you still win. Sivir whit this build will do exactly that. if your team understands it, its fine. If you play random you will get a lot of OMG, NOOB, Etc. If you can't handle that and not in it for the honor or respect of your team, nor care of having huge stats after the game but in it for a win. this could be your thing.

First you start of whit a Catalyst the Protector. You should be abailt to get it on lvl 5 and mabby eurlyer. Its passive regens your healt and mana on leveling so it is a ultimate item to keep you in line. then come the Ionian Boots of Lucidity. To up op your speed a bid and the cooldown. than comes the Gaint Belt. Just to counter any damage increasing items purchased by enemy hero's. The Philosopher's Stone is to get some mana and healt regen. Because the leveling wouldn't be going so fast annymore so the Catalyst isn't all that effective annymore. So its time to upgrade the Catalyst in to a Banshee's Veil this works wonders in could commbo whit your Spell Shield. After that you go in for the Phage and strait on to the Frozen Mallet. In combo whit your Boomerang Bladeand & Ricochet you can slow large nummbers of enemy's. At this stage of the game its not uncommen to be in 5 v 5 situations so freezing your ennemy's is a great ***it. Than you go for a kindlegem and combine this whit the Philosopher's Stone to make Shurelya's Reverie. This item has a great active in combo whit your ulti (On The Hunt). because it allso ups your teams attack. The reverie is on a 60sec couldown your ulti should be lower by know thanks to the cooldown of several items. Try to have ulti ready when the reverie is ready for juse for the max effect. To make your support role efen more effectife is to get the Emblem of Valor. And upgrade it to a Stark's Feror. Here I have also edit a Manamune Blade to up your magig damage. To get full effect your mana should be up a bid so thats why I splittet it up in Tear of the Goddess because of it's passife your mana whil greatly increase. But you could also chose to get Stark's Feror in 1 build and than get The Last Whisper but remember this is more expancive, and most game's don't last long enough for you to get the gold needed to complet that.

the build is 0-9-21 the 9 on defenc or to give you a advatage in the start and also to coplement Fleet of Foot. Sivir's caracter spel. whits is dodge change increast when moving. so if you need to get out you know also get speed benifit when you dodged. the rest is al concented on cooldown and getting fast ex and gold. Because Sivir is a carry her strengst are in higher levels.

The Greater Quint of Fortitude & Greater Seal of Fortitude should keep you from finding your self being in health problems in the begin stage of the game. If you fined yourself having health to spare you can change some Greater Seal of Fortitude for Greater Seal of Evasion to complement Fleet of Foot. As for the Greater Glyph of Focus you should be able whit the rest of the build to keep popping spell on spell on spell.
The Greater Mark of Desolation is to get your basic attack damage up a bid.

here you see i have chosen Clarity and Teleport.
Clarity speaks for it self i suppose. because of the huge cooldown you gain your mana whil drain fast. Using Clarity should help you to keep your mana on level.
(if you would find your self still in mana problems you could chose to bring Tear of the Goddess to the middle of the item build instead of at the end to up your mana total)
Teleport will help you to stay in line in the start. so you gain more XP and gold. later on this could be jused to move around the map quickly to support multiple friendly hero's.

As you can see. the sequence is set on Boomerang Blade, this is your main weapon. Because you don't have a lot of damage increasing items. also your Ricochet should be up a few level's at the time you get Frozen Mallet. getting Spell Shield to level 1 is for the start good enough. the next levels only help you whit cooldown but because of your build cooldown while automatically be gained. on lvl 6/11/15 you can level your ulti (On The Hunt) because this is a great support for your team and your aiming on that whit this build it speaks for it self that you should level this skill than.

your main priority is to stay alive, level as fast as you can and be a ultimate support unit.
Early-Game you should keep your self from dieing thanks to the extra health.
Mid-Game you should be tank't up whit live and have your Boomerang Blade maxed out. this is your main source of damage at this state of the game.
End-Game support you allies whit the Reverie and your Ulti (On The Hunt) to up there attack, and slow your enemy's whit the Frozen Mallet.