This is a high DPS build of Jinx. The build purposely lacks a lot of Attack Speed, and that's because of Jinx's Q minigun (Pow-pow) buff.

Pros and Cons:
+ Counters lane bullies, particularly Varus, which in themselves counter-carry. This is due to her kit of high damage skillshots.
- Uses up a lot of mana in the laning phase, mostly on Rockets and her E.
+ Passive makes Jinx a great sort of "hit and run" champion. Meaning, Jinx pulls off quick kills and gets away, really fast. Useful against turrets.
- Skillshot Ultimate. It's a powerful ultimate, I agree. But it's perhaps one of the most difficult ultimates in the game to use. More or less, lining it up. Moreso because you have to hit a low health target to get anything out of it.

Other items that work well on Jinx include:

Black Cleaver- I wish people would give this item consideration on ADCs (DPSCs). The Armor Penetration combined with the normal DPS building is substantial.

Statikk Shiv- Statikk Shiv combos REALLY well with PowPow's Attack Speed buff.

I have truly no items that I can think of that most build that don't work on Jinx...

Good-
Flash- It gives clutch mobility. Exactly what Jinx needs.
Heal- Heal is viable on any squishy champion. The healing ratio is higher.

Not Ideal-
Exhaust- This actually has a small amount of viability, but should not be used.
Teleport- You really don't need this, but it could help your laning.
Barrier- It gives you defenses, sure, but you always have the Flame Chompers to protect you...
Cleanse- It's alright. It can get rid of CC, which you can get in fairly easily. There's still the Zephyr though...

Never Use-
Ignite- If you are close enough to Ignite, you are also close enough to use the minigun.
Ghost- It's called GET EXCITED! *Crazed Psychopath Sound*
Garrison- THIS IS SPECIFIC TO DOMINION.
Smite- Well, more viable than you'd think. Still utter crud, however, on Jinx.
Revive- Unreliable, therefore unviable.
Clarity AND Clairvoyance- Unviable, in every way plausible.

Playing Jinx is actually fairly easy, in general.

1. Using Switcheroo!- This will be a bit brief. USE THE MINIGUN AT SHORT RANGE, USE THE ROCKET AT LONG RANGE. Simple. Greatly encourage the Minigun for tower dives.

2. Using Zap!- This one is also a simple ability to use, other than lining it up. The ability slows and gives sight of the target, for a few seconds. I use it to cross-lane poke, or to chase.

3. Using Flame Chompers!- Use it as a barrier, to run in other words. Or just to make the lane safer. Either way.

4. Using Super Mega Death Rocket!!!- Use this to pin down enemies low on health when you know the trajectory to them. Or to just crossmap, if that's your big idea.

In general, play Jinx kind of offensively. Her game throughout is good if you try to safely push the lane. Really, she's a simple champion. Extremely so, in this category.

Team cooperation with Jinx? Umm... I can tell you that a good support will be the one that has good stuns. The best support for Jinx is Thresh. The worst is a kind like Soraka.