Pros:
+100% crit
+Long range
+Tons of damage
+Great Wave Clear
+Teaches you positioning

Cons:
-No escapes
-Lose early trades with life steal quints
-Slow build time
-Requires good positioning

For ranked games, I would recommend against building your two Infinity edges first, and pick up a statikk shiv after the first IE. There are two reasons for this, 1) not every game is a double IE game. Honestly, the 100% crit is great late game, but some games there won't be a late game. If you are getting crushed, consider not picking up the second IE after building statikk shiv, and do not build phantom dancer with statikk shiv unless you are going for 100% crit chance. Good alternatives for ranked play would be to buy Last Whisper after Statikk shiv or bloodthirster depending on if the enemy team has built armor yet. 2) Your team may or may not rage at you if they see two infinity edges in your inventory. Since you are not following the meta, people will rage, especially if you are losing or things are going bad in the game. Make sure that you have a decent lead before deciding to get the second Infinity Edge.

White: Rito's ability description
Red: Leveling description
Blue: Tips and Tricks

-Whenever a champion, tower or inhibitor that Jinx has dealt damage to within the last 3 seconds is killed or destroyed, she gains 175% Movement Speed that decays over 4 seconds.

-This ability is great for repositioning in a team fight, and makes getting kills very satisfying. One of your weaknesses during laning phase is your lack of mobility, but if you can kill one of your opponents during the fight you can use the speed boost to make your escape. Sometimes it’s better to fight rather than run. You can make a lot of plays using this passive to barely escape with your life.
-Another place to use this is when diving opponents after tower kills. The speed boost can often catch players off guard, which you can punish them with flame chomps if you are ahead. Often times, you can get a kill if you coordinate with your support, setting the support up for easy skill shots to land on opponents trapped by Flame Chompers. You have to be careful though, and understand your opponent’s strengths. If you are not ahead of your opponent item wise, they can often punish you for being over extended, especially if you use Flame Chompers offensively and they turn on you instead of running. Another note, you want to make sure you have vision of the jungle before over extending, junglers could be waiting for you to overextend and without proper ward coverage, you will get picked easily.

Jinx modifies her basic attacks by swapping between Pow-Pow, her minigun and Fishbones, her rocket launcher. Attacks with Pow-Pow grant Attack Speed, while attacks with Fishbones deal area of effect damage, gain increased range, and drain Mana. Jinx swaps weapons.

Pow-Pow,the Minigun

Basic attacks grant additional Attack Speed for 2.5 seconds. This effect stacks up to 3 times for a total bonus of 30/55/80/105/130%. Stacks fall off one at a time and only benefit Jinx's first attack after switching to Rocket Launcher.
Cooldown: 1
-This gives a decent attack speed buff that scales to an insane amount. During lane phase, you can use this to push the wave and lifesteal. You will heal really fast if you don't suffer too much poke with your lifesteal quints. Using Fishbones, the Rocket Launcher, can lead to jungle ganks as you will be pushed up. Use the attack speed to win trades, lifesteal off of minions, and last hitting during laning phase.
-Late game, you want to use the minigun in team fights, mainly when an enemy jumps on you into minigun range, however, try to keep your distance and stay in rocket launcher if possible. A mistake I see players make is using their rocket launcher instead of minigun, even when they are being sat on by a tank or assassin, the attack speed will help you melt these targets faster if they are within range and you can't escape.

Fishbones, the Rocket Launcher

Basic attacks deal 110% Damage to Jinx's target and all nearby enemies, gain 75/100/125/150/175 range, and drain Mana.
Cost: 20 per rocket
Cooldown: 1
-This gives Jinx great poke in the lane, as well as a safe way of fighting late game. During laning phase, you can use this to push your opponent out, simply by doing more damage to minions than they are doing to yours. I would not do this too often however, because you will quickly run out of mana. Another use for the rocket launcher in laning phase is poking at your opponent. To do this most effectively, you want to watch for when they are going for a last hit, and switch to your rocket launcher, auto them once, and switch back to your mini-gun and back off. This is an easy way to get off free poke, as they will be stuck in their autoing animation, and will unlikely be able to trade back. A much more harder to master trick is switching between rocket launcher and minigun for a pure DPS boost during a straight up fight. Basically, your first auto attack when switching to rocket launcher keeps the attack speed bonus from minigun. By using this, you can auto attack twice while at 3 stacks of attack speed, switch to rocket launcher, shoot once, and switch back to minigun without losing any attacks. I would not recommend this trick to beginners, as you can easily get lost in which gun you are using or miss an auto attack if done improperly, but I thought I would mention it as a high difficulty tip for those who want to master jinx.

Jinx fires a shock blast that deals 10/60/110/160/210 (+140% Attack Damage) Physical Damage to the first enemy hit, revealing it if it is not stealthed and slowing it by 30/40/50/60/70% for 2 seconds.
Cost: 50/60/70/80/90
Range: 1450
Cooldown: 10/9/8/7/6
This is a great ability for poking in the lane, as well as catching opponents out during the late game. During the lane phase, you can catch opponents off guard by last hitting a minion and immediately using Zap through the dead minion. In early trades, you can win trades by auto attacking, and immediately casting Zap during your auto attack cooldown. This should only be done in the early game, as late game you will have a higher DPS by auto attacking due to your massive attack speed. You can use Zap to help your support land skill shots, or if your support lands a CC on the target, you can hit them with Zap for free. If your opponents are pushed up to their tower, watch to see if they run between the tower and the wall, you can punish them in this tight space by using Zap, as they will have little space to dodge it. Keep in mind, Zap has a considerably longer cast time than most other spells, this means that opponents can punish you for casting and you should be ready to dodge abilities after the cast. Late game, use Zap to help kite opponents and poke at a safe distance. You can also use Zap to face check bushes, if done at the proper angle you will either get vision of the opponent you hit, or force them to come out of the bush. Make sure you are at a safe distance, as it will be much harder to dodge skill shots if they come from the fog of war AND you are stuck in your casting animation.

Jinx tosses out 3 chompers that, once armed, explode on contact with enemy champions, rooting the target for 1.5 seconds and dealing 80/135/190/245/300 (+100% Ability Power) Magic Damage over 1.5 seconds to nearby enemies. Chompers last for 5 seconds.
Cost: 50
Cooldown: 24/22/20/18/16
Range: 900
This ability is a great zoning/CC tool. It can be used on choke points to force opponents to either wait for the chompers to expire or to find another way around. In a way, this is your best escape tool, and it only works by forcing opponents to run around the chompers if they are placed properly, giving you time. During the lane phase, use flame chompers defensively if you are getting ganked, try to block as many opponents as possible, giving yourself more time to escape. If your support lands a CC on an opponent in the lane, you can use flame chompers on them for additional harassment. Use your rocket launcher to poke them at a safe distance while they can't move, but be prepared for them to turn on you after the CC wears off. If you have your opponents locked down, you can follow up with either Zap or Super Mega Death Rocket, depending on your opponents health. Late game, use Flame chompers to zone out the enemies in choke points, or to protect yourself from enemy bruisers and assassins, blocking their path. Be careful though, throughout the game, people can easily flash over the chompers, rendering them useless, especially in the late game when everyone has their summoners off cooldown.

Jinx fires a rocket that gains damage over the first second it travels. It explodes on the first enemy champion hit, dealing 125/175/225 (+50% bonus Attack Damage) to 250/350/450 (+100% bonus Attack Damage) Physical Damage plus 25/30/35% of the target's missing Health. Nearby enemies take 80% Damage.
Cost: 100 Mana
Range: Global
Cooldown: 90/75/60
This ability is one of the best executes in the game, for its massive damage, AOE, and its global range. Its base damage scales with the distance it travels up to its cap damage. It hits damage cap at 900 range, equivalent to the range of Zap! You can pull off a fancy combo that may result in either a kill or a flash, by using Zap and quickly following it up with your ultimate. If you hit Zap, your opponent will be slowed and have little chance of dodging the oncoming ultimate without flash. Another great time to use your ultimate is when opponents are CCed, you can set this up using your Flame chompers. This ability scales with your opponents missing health, make sure you use it when their health is low, preferably below 35%. This ability has a long casting time, similar to Zap, and as such can be punished in the same way. When fighting an opposing ADC late game, if you cannot guarantee the rocket to hit, it may not be worth the cast, as you can lose 2-3 auto attacks to its cast time. Early game, if your opponents are low on health, watch your exp as you approach level 6. If their health is low enough, you can hit level 6, immediately dip into the side bush, and fire your ultimate at them. This can catch them off guard, as they may not have seen you hit level 6, as well as using it from the bush denying the vision of your casting animation. Late game, Use this in team fights to inflict massive damage, the lower the health of your opponents, the more damage it does, so it will melt targets with a large health pool, as well as those with smaller health pools and little armor. Since Super Mega Death Rocket has a global range, you can use it if you are late to a fight, if you get a kill or an assist within seconds of it hitting, you will activate your passive, helping you get to the fight. Be careful late game of your opponents flashing your rocket, if they are not CCed and can flash away, they probably will.

-My rune choice focuses on early game defensive stats, and late game offensive and sustain stats. Flat armor Seals and flat Magic Resist glyphs are pretty common and provide nice protection in the early lane phase.

Critical Strike Chance Runes

Since patch 5.1, the build now only give 95% critical strike chance, and since we want to avoid RNG late game, I take 5% crit chance in runes. During the lane phase, there is a 5% chance for you to critically strike. This can actually swing a fight in your favor, as no one expects the early crits. The downside to using critical strike runes is the lack of AD compared to your opponent. They will win straight up fights, and because of this you will need to poke to win trades and avoid all out fights.

Lifesteal Quints

These are mostly for late game, you may not be able to build a lifesteal item every game, and will want to replace Doran's blade. These give you the freedom to build other defensive items, such as Banshees Veil or Quick Silver Sash, or armor pen, with Last Whisper. In the lane phase, these do little in all out fights, but if you can poke at your opponent without taking damage a couple of times, you can push them out and heal minor damage rapidly. Late game, when you crit minions for 1000 damage, you heal for 45 with lifesteal quints, giving you quite a bit of sustain out of runes alone.