
Jinx is one of the best ADC's and is rarely countered (except by Graves). She is often picked in ranked games and LCS games because of how good she is.
Upgrading Abilities
When I play Jinx, I like maxing W first because it deals lots of damage and can slow the target by up to 70%. The only time I max out Q first is if the other ADC have abilities that can go through the targets (such as Sivir's Q or Kalista's Q) so you can be out of range of their pokes.
Using Abilities
Practice frequently changing between her rocket launcher and her minigun (her Q ability). When in lane or in a 1v1 situation, use her minigun since it gains passive stacks for extra attack speed. When in a team fight or in a fight against 2 or more champions, switch to her rocket launcher for the splash damage.
When chasing someone, use your W ability to slow them so you can catch up.
If they are very close to you, put down your E ability to stun them but you need to make sure that you give enough time for your chompers to activate. Never waste your E ability, because it is very useful to run away from other champions that could be chasing you since Jinx has no flash-like abilities (such as Ezreal's E).
Since Patch 5.8, her R ability (her ult) has been nerfed for short range fights. At her W range, her ult deals around 10% of what it normally does, so dont use it close range in team fights.
Items
I recommend you build some lifesteal first since ADC's have little health. Then rush Infinity Edge for the critical strike chance. Then build statikk shiv for the attack speed. Then build the bloodthrister for the large amount of lifesteal. Then build the Last Whisper against tanks. All these items can be switch around in order depending on the situation in-game.