I am currently Master adc player. Jinx is my favorite adc. Thanks to her I had 495 lp in challenger (unfortunately dropped, but working to get back there). Since having ~95lp I started spamming her in every game I could, thus making it to mentioned ~495lp. 

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COACHING

Remember that they have no cast time so you can use them while walking. Also remember that they need a time to arm themselves, so put them a little behind or after the enemy as a zoning ability (unless the enemy is cced).

You can see my standard runes for adc above. After last changes in rune system there is actually a lot of options here. I made this rune page immediately after last changes to runes and I am just too lazy to add more pages for adc. I got only one more page without attack speed, but with pure ad for Lucian. Regarding runes feel free to copy any runepage from pros - they are easy accessible. However, if you have time and like thinking about different sets of runes on every situation here is a small breakdown describing other options and when to consider them. The description is very general, not Jinx specific.

QUINTS:
You can change attack speed for pure ad for ability based champs like lucian/graves. You can change it for armor if you are running health seals and you are afraid of burst from your enemies (e.g. playing vs graves).

MARKS:
I don't see any legit alternative to ad.

SEALS:
There is a lot to think about here. A lot of people take some health runes here. Health > armor early. So if you are planning early all ins go for health runes. However the longer game is going armor is getting better. If you go for full health seals consider pairing it with 1 or 2 armor quints.

GLYPHS:
Similary to seals there is a lot to think about here;) The valid possibilities are attack speed and mana regen runes. Jinx is really mana hungry champion, especially early, so if you feel you need the additional mana early just swap scaling runes to mana regen. Personally, I do not like attack speed runes here since attack speed on quints is much more efficient and magic resist on glyphs is much more efficient than attack speed. However, I see some pro players running attack speed runes here. It is definitely to be considered when you do not fear any magic damage from your enemies.

SCALING OR FLAT:
Depends on how much you will exchange before 6. Scaling runes have same numbers as flat on level 6. So if you feel you need to be more tanky after level 6 go for more scaling runes, otherwise take flat. Still, almost never take more than 4 scaling runes, unless you go for lane swap. If you are going for lane swap you can even try going full scaling runes. Other situations when you should consider going a lot or full scaling runes are: 

• opponents on lane have no magic dmg, but other opponents does - take full mr per level (e.g.: jarvan support).  
• opponents will play defensive lane or present no kill threat to you - take more than usual or full mr per level (e.g: soraka support)

I can't think of any other regular valid situation when going more armor per level runes is legit since your enemies will always be able to auto attack you even if they are ap;) 
Summing up: going full flat armor and mr is better than going scaling runes in about 80% of the cases, because a large number of lanes on soloq is decided before level 6. The reason I got some scaling runes in my rune page is that I just really really like scaling runes;)

Jinx's passive
When I started to play Jinx I had been forgetting about her passive very often, but there are many situations it can be useful:

• you are considering tower dive, but you are almost sure that after kill the turret will finish you off - maybe it won't if you consider her passive?
• you are killing the turret and you are stronger then your enemies. Check if they forgot about your passive, if they did, chase them after getting speed buff from the dead turret (don't overchase, it is one of the biggest reason of throwing games).
• with Jinx passive it is sometimes ok to go out of position when chasing kills, but you have to be sure that you get the kill, so you can run with yive 

Jinx's combo
You basically need someone else to cc an enemy or an enemy who will pop out in some known by you place (fiddle after ult, mage after zhonya, someone with guardian angel after getting killed). You also need the enemy to not be blocked by any other enemies/minions. If all of this conditions are satisfied you go with e, 1 aa, w, r and 1 aa if not dead yet. It is best to do those aa with your rocket launcher since it does 110% dmg and attack speed from mingun won't help you in doing your combo. Of course if you know that you will need your minigun after combo, use it, to stack the attack speed.

Rocket launcher or minigun - it is a question
Before we answer this question lets see what are the characteristics, advantages and drawbacks of each of those two forms.
Minigun:

• big one target damage
• big lifesteal
• close range
• dangerous to use

Rocket launcher:

• one of the biggest adc range in the game
• 110% dmg
• aoe auto attack!!
• slow attack speed
• costs mana
• if you are attacking at least two enemy champions at once you deal more damage with rocket launcher than with minigun! (remember that attack speed steroid applies only to base attack speed)

Basically you should use minigun when you are 1 v 1. You should often use it when you are dove by 2 people and you know that you will be able to kill one if you use minigun and won't be able to kill anyone with rocket launcher (you got more 1 target dmg and more lifesteal with minigun, so you will live longer). If you can focus only one target, and can come to 525 range to him without being afraid use your minigun as well. In all other scenarios use your rocket launcher. 
There is sometimes a situation when you got your rocket launcher up but there comes to a situation in which you can swap it to minigun. If you know that you will kill your enemy in 2 or less attacks in this situation do not change to minigun unless you will be using it after the kill!! This is because minigun needs time to scale its attack speed, but rocket launcher has 110% dmg - so 2 attacks with it will deal 20% more dmg than 2 attack with minigun and won't take much longer.
If you are safe to attack with minigun, but you can hit 2 or more enemies with your rocket launcher, keep your rocket launcher up.

Jinx is weak early game. However, in most cases she can farm through it thanks to range on her rocket launcher. Rocket launcher autos cost mana, which is very painful, especially early, so don't waste them!! Try to cs with your minigun as often as possible. Of course, when you can't cs with minigun without being harassed use rocket launcher, when you want to push lane really fast use rocket launcher, when you want to safely harass enemies use rocket launcher, but always look at your mana while doing it!!

Since Jinx's w is hard to hit without your opponent being cced the best thing to harass enemies is by abusing her rocket launcher range. Remember that it has splash damage, so in many cases you can harass your enemies by hitting minions. Moreover, remember that the best moment to harass your enemy is when he is going for a cs (enemies know that too, so if you see that opponent is doing that it is usually better to miss a cs and answer back).

Jinx is starting to become a threat at level 6. You basically need to have a support with CC (leona/sona/thresh/morgana, etc.). You w8 for your support to stun enemy, use your e, 1 aa, w, r and 1 aa if not dead yet (covered more carefully in previous section).

Mid game starts when laning is over. Jinx has quite strong mid game. What you are aiming to do as Jinx is to push turrets. Thanks to her minigun she takes turrets surprisingly fast. If you won your lane just push the turret and quickly rotate to mid and then top. In many cases you will just be able to catch opponents off guard with your turret killing speed and win a game by that simple move. 

You have no escape so you will need to rely on your teammates peeling abilities and your positioning. You want to catch on your e as many people as possible (if you do it well you can win teamfight just by that). You also want to stack your ultimate with other AOE ultimates from your team - remember that you deal more damage the less hp your opponents have, so try to use it when enemies are already low. When you are about to die it is usually good to cast your ultimate just before dying. 

In team fights usually stick to your rocket launcher, so you can stay safe - try to damage with it more than one target at a time. However, if you are dived by enemy bruiser, tank, ap carry, anyone switch to your minigun for bigger dmg over time (covered more carefully in one of previous sections).

Jinx is a late game beast. What I have written in mid game section about team fighting stays here as well. However, if you have 4 dmg items (ie, pd, lw, bt) you do immense dmg. Unless you are dived stick to your rocket launcher, auto attack and dodge enemies skill shots. You will be surprised how much dmg Jinx can do late game!!

Videos are from my stream. If you want to see more videos I will be uploading them to my youtube channel.

Very nice triple kill showing Jinx's skill usage. Play Video
Jinx video guide based on a ranked game on my plat 1 smurf. Play Video