As I have some sparet time on my hands, I want to share some tricks and tips that I learned while playing the League. I will go champion by champion and tell you each and every trick I know about certain champion. As the epilogue, I will share a few other in game tricks that you can pull off with every champion. Enjoy
Akali - Her ultimate can be used to close the gap between enemy and you. Let's say an enemy is outside of your R range. Instead of aproaching and then casting ultimate on enemy you can cast your ultimate on enemy minion that is close to enemy champion. From that position you can freely jump to enemy champion and damage him.
Alistar - There is a similar trick with Alistar. Instead of using your headbutt on enemy champion, use it on minion, then when in position use Q to knock up your primary target.
Amumu - Amum has several interesting thingies. His passive on E lets him jungle very good. However if you invest some points in Tough Skin mastery in defensive tree, you can reduce that damage further and with later levels of your E, you can completely ignore jungle monster damage.
Another interesting thing about Amumu is the fact that he can kill baron Nashor by himself since his W damage is not capped against monsters. Since the damage itself is proportional to enemy health, no matter how much health Baron has, it will kill him in the same time frame with any ammount of health.
Anivia - Your wall can close the passage on dens where Baron Nashor and dragon are. You are actually having Jarvan's ultimate at your disposal. It is also interesting that old Sejuani could break Anivia's wall, with rework, Sejuani can't do that anymore.
Annie - If you have Frostfire Annie skin, your stun particle effect would be very hard to see which will give you a small advantage. Also, if you keep your pyromania stacks at 3, you can quickly press E to gain a charge and then use the stun.
Ashe - The longer her arrow flies, longer the stun. It can go up to 3.5 seconds.
Blitzcrank - If you press E and if your next attack critically strikes, you will strike for 300% of your attack damage. With inifnity edge that is 350%.
Ezreal - Whenever your team pushes a turret, fire Essence Flux over them to boost their attack speed. Don't forget that.
Fiddlesticks - He has the longest spammable disable. At level 5 it fears a target for 3 seconds. Also, if you use fear while under enemy turret, you won't attract turret aggro. Fiddlestick is also another champion that can solo the Baron with enough ability power and cooldown reduction.
Gangplank - Ravenous Hydra and IceBorn Gauntlet will proc their passive on his Q. Most people call it Splashplank.
Irelia - Irelia can use the same technique as Akali, dash to minion, then dash to enemy champion. However you must be careful not to aim at minion that has too much health or your Q won't refresh. Irelia will heal from her Hiten Style even when attacking turrets and inhibitors.
Janna - If you activate your Q in a bush, your enemies won't see the spell effects, it will charge at full speed on not suspecting enemies. Also, if you use your ultimate on the entrance at Baron pit, enemies will be knocked to the walls which will trap them inside.
Karthus - Never cast your ultimate while you are alive, if you want to, then hide or one stun will break your channeling. Also, if you put cooldown reduction on him, your Q will be a lot quicker to spam. Whenever you want to attack your enemies, place Wall of Pain behind them and then turn on your E. They have 3 choices. Burn flash, go through Wall of Pain or to engage you.
Katarina - Same as Akali and Irelia.
Kennen - You can cast your Q while you run with E.
Malphite - Thickest wall parts in mid lane (where the brush is located) are impassable by Malphite's ultimate, be carefull how you cast.
Malzahar - If you fight Akali with Malzahar, whenever she lands smoke shroud, use your Null Zone on top of that.
Nunu - Liandry's Torment is must have on every Nunu. Since his damaging spells slow enemies (E and ultimate) Liandry's Torment will deal 10% of enemy current health in magic damage.
Olaf - If you invest in some cooldown reduction and if you throw your axe in front of you, Undertow cooldown is 0.5 seconds. Also, if you activate your W and then use Smite, you will heal yourself.
Pantheon - While you channel your ultimate, you can queue up spells. Pantheon will immediately cast them when he lands. If you are losing while playing Pantheon and defeat is inevitable, you can sell your items and buy only ability power items, Rabadons mostly. Then use your ultimate in the middle of enemy team. They will wait for you to land to get an easy kill, however they will eat a 2000 magic damage nuke. It might win you a lost game. Pantheon is the best Teemo counter. Since he relies on spells and his passive blocks auto attacks, you can kill him very easy.
Rammus - Don't forget that his ultimate can damage structures (nexus, turret and inhibitor).
Renekton - He is able to proc black cleaver 3 times with enhanced Ruthless Predator.
Shaco - You can block some spells if you put jack in the box while spell travels (Mystic Shot, Rocket Grab). Whenever an enemy is chasing you, use your Q in the direction from which an enemy champion came, he or she will never even think to go back to search for you. Your clone will be able to proc black cleaver which will help you achieve max stacks much quicker.
Singed - If you chase an enemy, put Mega Adhesive behind you, when you fling them they will be stuck in the middle of sticky poodle.
Skarner - Always cast Crystaline Exoskeleton before your ultimate to travel farther, also spam your Q while moving.
Soraka - She can be very dangerous to enemy teams with Riven, Olaf, Pantheon or any other champion that heavily relies on spells.
Teemo - Put a Shroom in the bush, then stand on top of it. Hold still. If only a single champion arrives you immediately use Q on him when he hits the shroom, ignite, rinse and repeat. Also, never buy Nashor's Tooth and Wit's end both. Teemo relies heavily on Ability power, not on auto attacks.
Twisted Fate - Always prepare gold or red card when you want to gate.
Twitch - Innate, Red Buff and Spirit of the Lizard Elder. True damage, true damage everywhere. Also, his attacks won't damage inhibitor if you use your ultimate (possibly a bug), even if you specifically target inhibitors.
Volibear - His Q will damage turrets, same with Garen and Nasus. However it won't function with Jax or Kennen.
T key - Map one of your item slots to T key. On some champions you can roll a combo with Q-W-E-R-T.
Purple Ward - When you are fighting an enemy champion that uses stealth (Akali, Talon, Kha Zix, Wukong), put a purple ward when he or she uses his or her stealth ability.
Jungle Pull - When you are pulling jungle monsters, stand in front of them. This way golem or lizard will attack you, not your jungler. Your jungler will be grateful for that.
Baron-Dragon Aggro - If you are fighting near dragon or Baron, try to damage them and then pull back. This way a monster will attack enemy instead of you and will help you to take enemy down. This is very hard to pull off.