Overview:
Sivir is an AD carry that can push like a boss and help your team immensely in team fights. Sivir's primary use on a team is a ranged carry, yes. But she is very strong against and top lane champion who does not have a strong gap closer (so mostly pick as a counterpick). She has a spell shield to block poke and she can counter trade very hard with he burst. The general concept is a lot like Kayle top, stay back poke and farm as you will outscale 90% of top laners into late game.
Skills Overview:
Passive:
Fleet of Foot- Sivir's basic attacks against enemy champions grant her 50 Movement Speed for 2 secondsKeeps you mobile in lane after a trade, this skill will almost completely prevent a counter trade from the enemy champion if they have no strong gap closer.
Q:
Boomerang Blade- Sivir hurls her crossblade like a boomerang, dealing 80/125/170/215/260 (+75% of ability power) and (+110% of Bonus Attack Damage) physical Damage to the first unit and 20% reduced damage to each subsequent target. Cooldown 9 seconds. Cost 70 / 80 / 90 / 100 / 110 mana. Range 1000.Sivirs poke, use sparingly it takes alot of mana. This will deal really good damage i poke offs and in team fights allowing sivir to fit into either comp.
Note:The general rule of thumb is only use this as much as you can block with your spellshield. If you are not getting to spellshield skills, chances are that means the enmy is not sending any at you or trying to fight you with skills, in which case you should be able to auto them out of lane.
W:
Ricochet- Sivir's next basic attack will bounce to (5) additional targets, dealing (20/35/50/65/80) (+100% of attack damage) to the first target and (25)% less damage with each bounce (only the first hit procs item effects). Cost 40 Mana. Cooldown 7 / 6 / 5 / 4 / 3 Seconds.Her old signature skill. I Like it better in this form though, as an on hit it can reset your auto attack timer allowing you to deal tons of damage. :D This will allow you to deal massive burst if you get crit or a sheen. Its Low Cd and will give you more autos in a fight.
E:
Spell Shield- Creates a magical barrier which blocks a single enemy ability used on Sivir. Lasts up to 3 seconds. If an ability is blocked by the shield, Sivir regains 150 mana. Cooldown 22 / 19 / 16 / 13 / 10 seconds. Cost 75 mana. Range 20.The Skillcap of Sivir, This is where the good will be separated from the bad. This is a shield that can block skills aimed at you. This blocks single damage moves but will not block DoTs. This skill gives you mana for your harassing. If you master this skill you can block enemy trades and countertrade all day, if you miss it you end up wasting mana and looking like a fool.
R:
On The Hunt- Grants Sivir and nearby allies 25% movement speed and 30 / 45 / 60% attack speed (half for allies) for 10 seconds. Cooldown 100 / 90 / 80 seconds. Cost 100 mana. Range 1200 A good ultimate for pushing and team fights, gives everyone a massive attack and move speed bonus that can really change the game. Best part of this is in team fights since you were top you will probably have 2 AD carries to benefit from this ult :P.
Combos/Skillorder:
Max R>Q>W>E
Lane where you want to constant trade off high damage (Get an early
Vampiric Scepter if the enemy trades back decently strong.MAX R>Q>E>W
Lanes where the enemys main trade skill has a like 10 second CD allowing you to block it whenever he can use it.
In fights auto-W-Q-(E when they use skills) and (R to chase or go for kill)
Matchups:
Easy:
Garen(Cant catch you, his Q will not give him enough mobility early on unless he maxes it first, in which case you simply block that and his spin to win wont hit very hard.), 
Riven(You can zone her off early on, once you get your ult she is stronger until you get a 
Phage or red buff at which point you win the lane again), 
Shen (Surprised me too, You can block his harass in lane and keep him down with your autos. When he ults waya you can ult and push his tower hard.), 
Darius (A COUNTERPICK YESSSS, He cant get to you to hit you if you aut and kite, when you see him coming towards you, you can sheild and block his E and continue trading.) and 
Warwick (Can block his Qs with your shield if he ever gets to you, other than that you should kite him and you can shield his ult.).Hard:
Jax (He will destroy your soul.), 
Poppy (has armor and a nice gap close), 
Jarvan IV (Get dunked), 
Teemo (You can win early, but he gets very annoying with his poke his shrooms do give free mana though.), and 
Irelia (Good gap closer and strong commit).Playing As/Vs:
As:
-When an enemy blows stuff on your shield countertrade, they are down a CD.
-Give your ult to your team when doing any kind of fights, you will be surprised the impact.
-Use your passive to give you mobility to maneuver the lane.
-Poke with your Q whenever they have no minions in between you and them.
-Learn the range on your Q, if you throw it at the right position it can hit them with both the on the way and on the way back procs at the same time allowing more burst poke.
-Note:When fighting most Ad matchups without a gap closer it may be in your favor to buy a
Phage early on as to have complete mobility control.Vs:
-Stay behind your minions, her boomerang will do SIGNIFICANTLY LESS damage.
-Get ganks early, sivir is not as safe early on as she will be later.
-Deny the sivir farm if you do not she will scale into late game hard.
Big Item Choices:
Trinity Force- A Strong item on sivir top, I tend to get this in lanes vs enemys without a gap closer as it gives full mobility control, artificial crits (On a spammable W), and mobility and crit you love all of it in the top lane.
The Black Cleaver- Works decently with your shred, gives you AS and good damage.
Infinity Edge- Makes you strong in a fight.
Phantom Dancer- Gives you AS crit and MS very good for you.
Last Whisper- Armor Pen for when they stack armor
The Bloodthirster - Sustain and damage
Guardian Angel- 2 lifes on AD carrys are OP especially if you have like a thirster if they do not acknowledge and instantly kill you as you revive you will be a very big threat.Gametypes:
SoloQ:
You will most likely be called a troll for playing this here as most people simply do not understand that it works. If you get an understandable team you will be very strong later in if they help you and don't just troll "because you are trolling". Late game you will be able to carry and make your team go O.o sorry. :D
Ranked 5s:
THIS IS WHERE THE PICK SHINES! In here you can first pick Sivir and if you get a good lane opponent you can keep her and if you don't just trade it to your bot. Alternatively you can tell your friends you are going top, and pick something easy to counter. When the enemy team picks surprise surprise they are fighting a sivir top and a kill lane bot :D.
Conculusion:
I hope this helped you to realize that sivir can be a strong pick top. Do not let anyone tell you anything otherwise. She is a very underrated very strong top laner that needs way more props then she gets. She can split push, poke team, or just work on the standard direct commit team.
SERIES UPDATE:
I plan on releasing these every day/other day until I get all of the top lane picks in the league if there are any requests leave in the comments below and ill work on them. I want to make this series for others to better understand the champions of top lane. Once I am done (Or once I have a few top facts out) I will release some Facts about top lane mechanics, eventually I will probably put everything into one generic top lane guide, however until I do that I will continue to watch and update my blogs as needed. Tips and tricks I missed under my Top Facts would be helpful if you put anything I don't have in the comments I will be sure to add it. Thank you and have a nice day:P
Decisive Strike
Blood Scent
Judgment
Valor
