This is a basic item list, mastery list, and rune page for playing jinx competitively.
The guide also includes some tips on using her abilities.

Pros:
Has good cc that can hit more than 1 target
Has a global ult that acts as an execute
Has a passive that can be used to chase down low enemies which is very helpful in team fights
Has long range poke
Cons:
No escape abilities
Players find switching between her Q to be difficult

Here are the basic runes, many other players run something slightly different based on preferences such as putting in a few health yellows, or attack damage quints in addition to the ones I have listed. Personally I find the health not to be very relevant and the attack speed makes lane phase easier.

Q- Use your rockets to poke enemies in lane and before fights but be aware of mana use.
To keep the attack speed buff on Jinx you can attack 3 times with the Gatling gun, then switch to rockets (attacking 2x) then switch back to keep the 3 stacks.
W- Zap is a great ability to poke but it is even better as a means to initiate on enemies due to its powerful slow. Zap also grants vision against stealth champions.
E- Placement on flame chompers is crucial, DO NOT place chompers directly on an enemy champion they are not instant! Instead place them slightly in behind or in front of enemy champions depending on the direction you think the will be headed. Chompers can be used to gain vision in bushes.
R- Mega Death Rocket is a great execute, use it when enemies are low to secure kills. This ult provides good help for other lanes who are amidst fighting.