My list of tips.
I've been playing this game and games like it for a very long time and I have knowledge of a lot of tricks that can improve your Gameplay. So here's a list that I'll update as I remember tricks. Some of them will be "Yeah duh" but I hope I throw one in that you don't know.
1) Never miss a bush Ward again.
When you go to ward the edge of a bush, wait for your cursor to turn from blue to green, it only turns green when the ward will go inside a bush.
2) Flash doesn't have to be smart casted.
When you need to make a precision flash, you can left click the skill and the range indicator will pop up and you will flash where you click. This may sound like a dumb idea, but when you're being chased and need to know exactly when a flash will go over a wall, it can prevent that fail flash.
3) Landing skill shots
Skillshots 1) There are a couple of exceptions, but generally speaking, if you are using a line projectile skill shot, you want to aim for hitting 1/2 - 2/3 range shots. The reason you want to go for those range shots is 3-fold. First of all, it cuts down on the time your opponents have to react. This is the most obvious reason of course, but if you go for full range your opponents will have tons of time to react. The second reason is radial motion. When an enemy is really close to you, they can very quickly move 30 degrees off your aiming point and your skills are more likely to miss. The third reason is if they try to run away from you, they'll still be hit in most cases.
Skillshots 2) fire skillshots along lanes or down thin alleys to maximize your chance of hitting. So we've all seen the Jinx or Ashe ult that hits someone a mile away down mid lane. This is no accident. It hits because they cover a gigantic area when fired like this. Considering champion hitboxes, they hit close to 2/3 of the lane when fired directly down the middle. So unless firing down mid or the river, don't try to hit diagonal skill shots too often.
4) Testing damage
There are a couple of ways of testing damage. Minions are good and generally your auto attack is the best way, yes even for mages. This will help you farm, judge your ability to finish someone off, know when you're safe or when you're gonna die. So every time you get a new basic ability that deals damage, you should auto attack a minion and then use it on the minion and compare the damage it does. Generally it will do comparatively identical damage to champions, so knowing how your AA and spells compare means you can hit an enemy once and immediately know within a few percentage points how much damage your abilities will do to them if you blow everything. Testing damage is one of the best ways to know where you stand in an engagement.
5) When kiting or chasing as ADC, use audio cues
Your brain reacts slower to visual information than auditory information. This is a very well documented phenomenon. So you should always be listening for your auto attack and get in tune with the rhythm of the attack delay. So when you're chasing you will be able to click, hear the attack, move, feel the attack delay out, click, hear the attack, feel the delay, click.
6) farming under tower
So a lot of people have trouble with this one but it's not super hard to do if you know a couple of rules. Let melee minions that aren't being hit by other minions get hit twice by the tower and then attack them yourself. If they're being hit by other minions, hit them once early and again after the tower hits them. Unless you're an AD character with a bf sword, pickaxe, or some other big source of AD, you're going to have to set up the back line for farming. So to do this, you have to either use a weak (less than 90 damage early on) aoe spell on the back line or as you farm melee minions hit the back line minions once each during the first hit of the tower on the melee minions.
That's it for now, I'll update the thread and bump it over time. Hope these tips help.