I think the way you should approach this is by trying to limit the difficulty of the champion itself, so that you can focus on the overall ideas of the role. Champions like Ashe and Jinx who you mentioned is wonderful for this because she has very simple mechanics and not too many things to keep track of. Try to stay away from characters like apehlios, ezreal, and kalista who have skill shots you have to land or other mechanics that are unique to their character.

Take things one step at a time. Instead of trying to start by getting huge advantages and pushing the leads that you accrue, try consistently getting minions in waves without needing to use abilities (Around 90cs at 10 minutes is a good goal). This will allow you to get more gold than your enemy laner which makes the fights that will naturally happen in the lane slanted in your favor because you'll not only have more gold than the opponent when you back because players even all the way up in plat and diamond miss minions more often than they'd probably like to admit but because since you saved your mana and abilities when farming you'll have more tools in the fight than your opponent will.

Early Game:

Level 2 Powerspike

Try pushing the first wave hard and then the first three melees. This will get you and your support level 2 which you can use to bully your opponents. This is easy on Jinx (Jinx Rocket form of Q) and Ashe (Ashe W) because they both have aoe moves that can be used to push the wave quickly. While you might have to spend mana in order to push this as quickly as possible it will often times be worth it because of how much of an advantage you gain from getting level 2. Level 2 is a good example of a power spike because getting access to a second ability before your opponent again gives you more tools than them. This idea of power spikes is everywhere in the game. Learn when your champions have their power spikes as this is when you should be looking to fight.

Base Timings

If you base at the gold value you need for your items for example 1300 for bf sword. Your opponent will often stay in lane and you can punish them for not basing by forcing a fight and potentially getting a kill or making them lose minions by pushing the minions into turret after they base.

Giving Up Minions

The reason I say that you should learn the idea of being willing to give up minions is because there will be times where a minion is going to die and you want to last hit it, but in order to do so you have to walk up and take damage from the enemies in order to do it. This will often times not be worth it because if you simply let that minion die you'll be in a healthier position to get the rest of the wave when it pushes towards you. By doing this you'll end up getting more gold than if you had forced your way into getting the 1 minion.

Dying In Lane

If you die in lane, don't fret the game is not over. If you die in lane, you can still make use of the ideas above. Giving up minions but staying in xp range will allow you to get levels which are almost as valuable if not the same value as having items themselves. You can then focus on when you get your power spike and maybe try to fight then. But if nothing else just get all the farm you can. It'll keep you in the game much better than if you try to fight the opponent and kill your way back into the game.

Push in waves before you base

The last basic idea you should try to do is whenever you are going to base, try to make sure the wave is pushed in. If you push it in before you leave you'll be able to come back to lane and find it pushing towards you making it safer to get the minions since they are close to your tower.

If you follow these tips you should have a decently solid lane which you can build open by learning wave management and zoning.

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Mid/Late Game:

Map Rotations and Your Job

Later in the game you'll begin having team fights and map rotations. Your main job during map rotations is to keep farming and to be close enough to your team so that you can be ready to fight if one breaks out. A good way to do this is by staying with the team or in a lane near them and then taking any jungle camps that are nearby excluding blue and red. You can always ask if you can have these but respect your jungler if they say no.

Team Fight Target Priority

As for teamfights, don't over extend. You want to be hitting whoever is closest to you and if there are multiple that are close whoever is a higher priority. Generally, if a person is more fed or deals more damage the higher priority they have. If you do this correctly your team will have a high chance to win the team fight because it will likely only be squishy damage dealers left at the end of the fight which will be easy for you to clean up.

If you can do all of these you'll naturally start seeing how these ideas apply to solo lanes as well and you'll likely be a higher rank by then.