Jinx is a fantastic champion who can be very fun in lane and deal massive amounts of damage late game.
Laning:
While she does have a poke that slows and a snare in her kit, I find it best to not look to start engages in lane. You can leave that to your support and your enemy. I say this mainly because Jinx has no escape in her kit. If you use your zap and traps to go in really hard then you have to defense for when their jungler comes in and turns it around. This being said absolutely go for it when your support lands cc. Your main goal in lane should be to be passive with Jinx. She doesn't have the strongest early game so you should just try to get out of lane the laning phase as soon as you can.
Post-Laning:
Right Click on Enemy. Don't listen to your teammates when they tell you to focus Draven or Syndra, they have no idea what they are talking about. As ADC you have the ability to deal massive amounts of damage based 90% off of your auto attacks. This means that you should do your best to deal safe damage to the enemy. Lvl 9 and onward with jinx you have 700 range with your rockets which makes it very easy for you to take pretty safe shots at the enemy Malphite/Maokai. My very first pentakill in ranked I didn't get by killing the carries first. I sat in the backline firing out my critrockets to do an ***ton of damage to the grouped up tanks because they were the closest ones too me. Once you have LW you will be able to shred through the tanks that will mess you up with cc and then pick off the vulnerable carries afterwards.

Max Q first. This increases the attack speed from her minigun and the range and bonus damage from her rockets. Have a longer range is the best thing because it lets you be a lot safer when poking with your autos. As a general guideline when going for single-target kills you should start with your rockets and then once in range change to your minigun for the increased attack speed. Only keep with rockets if you really need to keep your distance and the enemies are grouped up. Remember your rockets do splash damage so you can shoot minions near the enemy and still do damage.
Take E lvl 2. If you push quickly in the very beginning of laning phase you can hit lvl 2 before the enemy and surprise them with snares behind them while you shoot them with your minigun (increasing attack speed).
Max W second. The zap is a useful poke and has a badass slow with it but for whatever reason will sometimes double as a tractor beam for minions, so be careful not to waste your mana.

Pros:
-700 Range and splash damage makes for the best teamfighting ADC IMHO
-Attack Speed from minigun makes for decent dueling potential and incredible turret killing power
-Having the slow and snare in her kit gives her a lot of cc which is useful
-Global Ult makes for great cleanup and sexy kills
Cons:
-No escape (caitlyn net, vayne tumble)
-Extremely Vulnerable without frontline of tanks.