#1. Warding, and vision control (and by extension, map awareness).
This is by far one of THE most important aspects of League as a whole. If you can see the map, but your opponent can't, you have a distinct advantage over your opponent when decisionmaking. This spills over to the next few segments, but essentially, learn your ward placements (tribushes, "hidden" ward locations, etc.), know where your opponent places their wards, and plan accordingly.
2. Map rotations and objective play
This is somewhat linked to vision control. Being able to rotate properly when taking objectives (Dragon, towers, etc.) is paramount when succeeding at LoL. Proper warding helps you when deciding when and where to rotate - if you've pushed bot lane, and the enemy turret is about to go down, usually your opponent will send someone to clear the wave. However, if you see multiple people (through proper ward coverage) going bot, and Dragon is already down (so there's no risk of losing it in the process), you have free reign over a strong top push or a Baron call - especially if they don't have TP available - something that might've been infinitely more risky if you didn't see the enemy team.
3. Major timers
3a) Gank timers
Usually, before minions spawn, both teams will play what I like to call "the ward dance" - placing strategic wards at jungle entrances to avoid invades. This can help you glean invaluable information - for example, where the enemy Jungler is starting. If you know approximately the amount of time your opponent will take to clear camps, you can more or less time when he's going to start ganking and play appropriately. This is usually learned through experience.
3b) Summoner Spell Cooldowns
Tracking enemy summoner spells is very important when it comes to decision making around picks and plays. If you know the enemy's Flash is down, you can go for a more aggressive play through coordination with your Jungler. This is doubly true if you have proper ward coverage, and know where the enemy Jungler is. For example, if you're on blue team and near botlane, and you know the enemy jungler is near his red buff (so he's near toplane), you can coordinate a towerdive gank bottom safely, knowing they can't Flash away, with the enemy jungler being nowhere near enough to help.
3c) Spell rotations
This is moreso true for laners - if you know your opponent's CDs, you can plan more aggressive plays around his downtimes. For example - if Ahri just use Q and W for clearing a wave, you know that, as long as you dodge her E, there's absolutely nothing she can do to retaliate outside of running away, auto attacking you, or if you're with your Jungler, Flashing away. This ties into 3b).
4. Making picks
This is pretty much related to 1. If you've warded up properly, and you catch someone out of position, you can pick up a quick kill, which can snowball into other objectives.
That's all I can really think of at the moment. Master these and you're on your way up the ranks, my friend. Of course, experience > theory, and it all comes down to putting everything into practice. I'm around Gold level, so I'm only pretty average at the things I've listed above, so I can't really say anything other than good luck, man.
