Evolve your thinking. Know that you and everyone else makes mistakes. Think about WHY a person did what they did. Just being receptive and looking for reasoning behind every decision without having a "I'm better" attitude will already put you into silver in due time. But for some general tips:
Main as 3 different roles, with at least 5 champs for each. But be sufficient with 1-3 champions in the other two roles. If you can play every role, then you know what each role does and why it does it. That is absolutely priceless information in this TEAM game.
Instead of calling "I'm Mid". Say, "Mid Pref" or "fill".
Instead of saying "Gank my lane", say "gank please"
Consider jungle routes you take when jungling. Enemies and allies do it too. Where would a WARD be placed to keep YOU from ganking?
For top lane, its mostly river, and tri-brush for purple. Blue side can consider river/land for river sight and blue buff sight, but needs to ward purple's tri too then.
For mid, if you don't actually get wards, use your trinket in a brush or tri area near either wraith camp. Play closer to that side.
As ADC, you almost always are the brush warder after your supp's trinket wears off. You can also use it in the river brush or tri (as blue).
As supp, start with a ward and either a red or yellow trinket. If you start red, you better wait till you see a ward go down before you use it. Better still, if you can distinguish if it is a ward or a trinket that went down. (know what items enemies have). If you start trinket (like 99% of the time) your trinket will be in the brush, depending on which side needs it. Don't rush placing it. See who is going to push first. Use actual wards in the river/tri because you have less opportunity to go there. Consider placing wards further out and in places that champions have to pass for a gank, but aren't common anti-ward spots (ie, don't ward dragon in his circle or right infront, ward next to the land across from it.)
If you see a enemy ward go down, Ping where it landed and say "river warded" or similar. This helps junglers immensely to navigate in a stealthy manor so as to gank successfully.
Speaking of which, junglers don't actually need to gank sometimes. If you see a ward or know a ward is there, you can kill it or run past, and then do a double take and go around the ward stealthy to another lane. The lane you were headed to knows you are near and will let your allies be safe a minute. Meanwhile, other lanes think you are there as well and will overextend. Take advantage.
Pay attention to where everyone is on minimap, and who has teleport. If you see jungler on minimap in any other lane, you are almost guaranteed safe for up to 15 seconds after they leave minimap vision. Take advantage and push during that time. If you don't know where enemy jungle is and your lane is pushing, either burst down the whole wave and run back to safety (don't even try to hit their turret) or take the time to ward, or at least play further back, enough so that the enemy mid can't gap clear to you with a flash+skill.
If you are being zoned to one side of a lane, that is the side they want you on. Prepare for gank.
If opponent acts in a way inconsistent with how he has been the past 5 min. (ie doing bad and suddenly sets up for an aggressive push) Prepare for gank.
Learn to gate mana use effectively, as well as Cooldowns. A blitzcrank that already used his Q is basically useless for 10 seconds. Save your skills for when you KNOW that you will hit. Also, most of the time, level 1 skills should not be spammed for damage anyway. You gain levels pretty quick and the mana cost for that early damage makes you OOM much sooner then your opponent. If you wait for a skill to be lvl 2-3, it does 50% more damage for 20% lower mana costs. etc
Keep track of enemies' play style. Which direction did they dodge last time? Do they bee-line for turret? Did they aggressively engage you when you were near their attack range? Did they chase you? You can use all these to set up ganks for your jungler, or use multiple skillshots to trick an enemy into dodging into the worse of the two... etc