Just a basic build for Sivir. Mostly for my own use (So I don't forget it), but you're more then welcome to give it a shot and try it out. Gonna make it a tad guide like for those who will want a more "expanded" build :P

Sivir is a pretty versatile champ, but so far I've only noticed a few summoner spells being worth a damn.

1. Ghost is handy. Good for chasing or escaping.
2. Flash is handy. Good for chasing or escaping.
3. Exhaust is good for slowing down champs and getting the kill OR for running away.
4. Ignite is also good for getting first blood when they run away from you.

Some situational ones are:
1. Cleanse, just in case the enemy team is CC heavy. Though if they are, it shouldn't make a difference because you've been slowed enough to become the next corpse.
2. Clairvoyance. I wouldn't take this unless you are a PRO at Sivir. This skill can be godly in the hands of a good Sivir, but you lose the benefits of the other spells from above.

You want to start out with Boomerang Blade to harass enemy champs in the beginning. Try not to use to too much, as it costs a ton of mana and Sivir doesn't have the best mana regen in the world. Then, when you level up, get Ricochet to farm minions, and to potentially harass them. If you're doing well, or get first blood, you might have enough for your Tear so you can probably leave this on and only use Boomerang Blade when absolutely necessary. The third skill you want is Spell Shield. Ah Spell Shield. I love this skill. It's so over powered early game it should be illegal. Perfect against enemy champions who have ranged stuns that take a bit of time to get to you. This skill you will only need one level in for now, but that one level wills ave you if you use it well. After that, you want to max Boomerang Blade first, then your ult, On The Hunt should be a close second to priority. Then Ricochet and lastly Spell Shield

On The Hunt is Sivir's Ult. While it's a great speed boost and attack speed boost, you want to save it for Team Fights and Tower Killing. Do NOT use it to gank one or two champions, and DEFIANTLY don't waste it on one lonely champ. Let your items make short work of them.

Start out with a Meki Pendant and two Health Potions. Build it into a Tear of the Goddess, and then build Berserker's Greaves. Now you rush the Infinity Edge, which if you're doing well, shouldn't be too hard to get. Then build the rest of the items up as you get the gold. Then go to town ;D

IF you need to, you could always trade out the Manamune for something like a Madred's Bloodrazor, Banshee's Veil, Sword of the Divine, or Frozen Mallet.

Try to do your best to stay alive and conserve mana as much as you can. If you are 100% sure you can get a kill, then by god go for it! The more the enemy champ is out of your lane means more farming!

By now, your build should be either halfway through or near done with the IE. This is when it'll be a tad easy going on mana, but still, don't be stupid.

By now, everything should be team fights. This is where you NEED to keep Ricochet on at ALL times and pop your ult when the two teams clash. Your ult can, and most likely will, change the course of the battle.