I'll address the three points you mentioned in your post: "switching my guns, ulting, and throwing down my chompers at the right time." I have a ridiculous amount of time on Jinx, so I think I know enough to help others as long as I can word it in a way people can understand. Without further ado...
Switching your guns: Jinx's Q, Switcheroo!, allows her to switch between her two primary weapons: Pow-pow and Fishbones (or Shiro and Kuro if you're a magical Jinx main). Here's some technical stuff you might want to read:
Fishbones, the Rocket Launcher: Basic attacks deal 110% Damage to the target and nearby enemies, gain 75/100/125/150/175 range, drain Mana, and scale 25% less with bonus Attack Speed.
Pow-Pow, the Minigun: Basic attacks grant bonus Attack Speed for 2.5 seconds. This effect stacks up to 3 times for a total bonus of [0]% (bonus scales with spell rank and Jinx's level). Stacks fall off one at a time and only benefit Jinx's first attack after switching to Rocket Launcher.
Essentially what this means is that Fishbones is great for long range, short duration poke, while having a splash effect. You can use it for last-hitting low health enemies that are far away, and you can even use it to soften up enemies AND farm, because of the splash. However, Pow-pow is generally best for farming when possible, so you can conserve mana for your other spells. Additionally, if an enemy tries to fight within Pow-pow's range, Pow-pow is best for that short range single target damage. However, fighting with Pow-pow isn't always the best option against something like a Vi or Kha'zix. That takes me to our next point:
Throwing down chompers at the right time: Sometimes you have to turn tail and get out of a bad situation. One of the things as Jinx that comes with experience is timing knowledge: How fast is the enemy moving? How fast will my chompers activate? By figuring these out quickly, you can determine where to place your chompers to buy yourself some time from your pursuer. Just remember that they can flash over your chompers if they're good enough, and so never assume that chompers=safe. Also, if someone towerdives you, you can place chompers if you know you're going to die, and take them down with you. It's great for when Vi ults you under your tower, kills you, and then tries to walk away, instead hitting a deadly trap that leads to you trading their ult for... nothing. It's great.
However, the chompers' purpose isn't just for deterring an angry Vi. If you have an aggressive support (which are usually better for Jinx), you can place chompers behind the enemy as your support stuns/hooks them. This cuts off their escape and can usually net you a kill. For an example, I'll use Thresh as your support. A good combo is for Thresh to hook, and as soon as you hear the sound of the hook connect, put chompers directly behind the victim, between them and their turret. You should then get in Pow'pow range and start firing, while attack moving towards them to close the gap. Once Thresh's CC is done, the enemy will either run into your traps or be forced to go around them (or flash). This means that they should still be in Pow-pow range, so you can continue shooting them down. Continue chasing them with Pow-pow until you reach their tower range or the 'danger zone' of their own support, at which point you'll want to fire a Fishbones rocket, Zap, and an ult if they aren't dead yet. Sometimes if the enemy support isn't there, you can flash and heal to stay in Pow-pow's range while under turret and taking fire. This is a risky play, but if you have confidence in it, the tower dive can sometimes be worthwhile.
Finally, ulting: As Jinx, you should be looking constantly at other lanes, trying to spot out low health enemies. This can be difficult to do while farming, but doing this can lead to kills you wouldn't have gotten before. However, don't look at a low health enemy and immediately ult; using Jinx's ult can often be a waiting game. The best way to hit the ult is to predict where an enemy is recalling, as it is during the recall channel that they least expect to be hit by a giant rocket of death (also they aren't moving). As soon as you see a low-health enemy enter the fog of war past their turret, it's a guessing game. And you have about one second to guess and shoot, or you'll be too late on hitting the enemies across the map.
This isn't always the way Jinx's ult is used. Sometimes, especially if you're not confident in your sniper skills, you should just hold onto it for finishing off your own laner. If you have a blue ward (which you should once you hit level 9) you can ward behind their tower, watch them panic, and then watch as your rocket of death hits them in the face.
I hope this was helpful and I didn't forget anything important.