First, really just play more games, get up to lvl 30.
While you do focus on these three things and get really really good at them:
All seem really simple, but are incredibly underrated when learning to play.
First: Last Hitting
- learn the differences in last hitting with the champs you play the most.
- for example: Leblanc is notorious for being incredibly hard to farm with and her last-hitting is much different than when you're trying to last hit with say, Caitlyn.
- always focus on staying in a good position and getting minion kills over trying to harass your opponent when in lane (and not supporting of course)
- seriously, last hitting is something that you have to constantly work at with every champion in lane.
Second, Map Awareness
- get in the habit of constantly looking at your mini map every few seconds
- though "MIAs" are helpful, in the end it is not your teammates responsibility to call mia's, so never-ever complain about that, if you missed Mid leaving their lane when adc bot lane, you need to work on your map awareness.
- know where and when to place wards (this includes if you are an AP or ADC) warding is a team responsibility and not just for the support.
- always know where your team is, where the enemy team could be, and where you should position yourself. Don't lose team fights because you wanted to farm top when you should have been mid helping hold your tower with your team.
Third, Not Dying:
- As you are leveling up and trying to improve always always always prioritize staying alive over getting a kill. Just do it.
- If you are trying to play adc bottom lane, don't try and be super carry and over-extend yourself, always play safe and focus on farming. When you do this you put your enemy in a position where they're more likely to make a mistake because they're probably just focusing on "kill kill kill"
- Even though it's really unlikely to happen, try and always play games to get zero deaths. (That doesn't mean sit at your fountain the whole game, actually play the game and try to win the game) but do what you can to minimize your deaths as much as possible.
Obviously there are many many more things you can do in addition to help improve your play, but I guarantee you, if you learn how to do these things as you're leveling to 30 really well, you'll outplay a LOT of other players you come across, because it's surprising how few players focus on these mechanics.
Hope this helps.