This is my first build so please be nice!

To start things off, this build is a lot different from other builds that I've seen because of one reason: Ricochet over Boomerang Blade.

I chose Ricochet over Boomerang Blade for two really good reasons:
1.) It costs way less than Boomerang blade in mana.
2.) It's an active so it has no cooldown and can be used at all times.
3.) It's is a way better harasser than Boomerang blade all game long (early, mid, and late). Unlike Boomerang Blade, Ricochet can't be dodge by moving to the side. You're going to get hit by it unless you have a dodge percentage that takes effect on that hit. this makes it much easier to harass players since you don;t have to concentrate on hitting them with boomerang blade. You can simply farm and let the bouncing do the work for you!

Gameplay wise, I always like to start off with a Meki Pendant and two health pots. I usually solo mid lane since I want to farm my build up because it is kind of expensive you know. Early game shouldn't really be a problem for Sivir since Ricochet will help with farming and harassing (so long as you don't get laned against someone like Teemo; he's a really mean girl!), and Spell shield will basically ruin any chance of the enemy harassing you back (this is especially good against heimer, gangplank, teemo (but his Toxic Shot also procs Spell shield (I think)) while giving you back mana for keeping Ricochet active.

Usually I'm able to push towers pretty well, and especially at level 6 when you're near tower with a group of minions (that has a cannon in it), use OHT/Ulti (On The Hunt) to get the minions attacking faster (and yourself ofc [of course]) to get that tower down.

After the first tower's down (if all is going well), blue pill (recall) back to base and grab Berserker's Greaves. These might not give the greatest chasing power, but that's what Exhaust is for, and the occasional Lizard Buff. If you still have some cash on hand, grab two Vampiric scepters (these will be used later to buy your Bloodthirsters).

Now you should be really sent since you now have 24% lifesteal and the extra 25% attack speed(AS) increase. At this point you can help other lanes if they need help pushing, or you can farm in the jungle for a bit. Make sure to keep an eye on mid lane though, because that's your lane and you still have to defend that tower! Keep farming up your items and go back really only when your team doesn't need you to push (i.e. you've killed most of the other heroes on the other team and are pushing, or you've just killed a tower).

Basically, just keep farming up items, help your team push, and especially kill some heroes when you get the chance. It's really not all that hard to play Sivir since she takes no skill with Ricochet active all game and can farm like a muther, so that's about all I have to say about this build.

Comments/Concerns/Suggestions are welcome. I'm not completely sure about glyph runes, but I'm sure there is probably a better choise than CDR (Cooldown Reduction)