the concept is very simple, yet its hard to execute and needs careful examination and practice:
Wave control is about steering where the minions are between your turrent and the enemy turret.
As a quickstart: Enemy minions are always spawing the same time than yours. They are exactly mirrored. this way, if you look at your own minions, you know where the enemy minions are:
¶ Shoving the wave (into the enemy turret)
When you are pushing the minions towards your enemy, you apply pressure. You are open for enemy ganks, which is very dangerous.
In such a situation, Be wary of enemy ganks.
Try to kill the enemy minions asap (safely). Once no more enemy minions are there, they will "shove" into the enemy tower. The tower attacks them and denies gold to the enemy.
You will have level advantage usually (because you killed the minions before the enemy).
When both minion waves (yours and the enemies minions) died before new minions arrive, congratulations. you achieved a lane reset. The minions will collide in the middle between yours and the enemy turret in a "neutral position"
The cyan line marks where the minions will colide at after the push.
Be careful when shoving, as the enemy might freeze the lane (next explanation). also be very careful where the enemy minions are. If they are just approaching while your minions shove into the tower, they will stop briefly, attacking your minions. Causing your next minions to run up close to the enemy turret, where you can either not farm the enemy minions under turret or you are back at square one, open for enemy ganks.
The cyan line marks where the minions will colide at after the push.
¶ Freezing the Lane (opposite of shoving/applying pressure)
Playing defensively is (often) a favourable move, if you can sustain it.
You do that by not attacking minions at all, only dealing the last hit to them when they are at very low health. This takes practice. Try to avoid area damage on them.
-> The enemy is attacking your minions and applying pressure.
-> The enemy is now in a vulnerable position, open to allied Ganks
Make sure to adjust your farming speed to the enemies farming speed so that you do not get overwhelmed by a big enemy minion wave.
A rule of thumb is to let the enemy have 1-2 more minions than you, for a slow push towards your turret. Maintaining this ratio is called "trimming the wave".
Try to keep up with the enemy push speed. If nessecary, use area of effect damage spells, as they are usually very effective against minion waves.
When your minions die, and the enemy has 1-2 left, you can distract the enemy minions by walking close to them, so they do not run into your turret.
What will happen next is that your wave approaches them and you can "freeze" the lane in front of your turret, opening the enemy for ganks of your jungler, or assasinations.
In case the enemy minions do reach your turret, be patient, decide well.
You can attack the ranged minions first (if you are ranged), as they have the lowest health. The goal is to reduce the enemy minion count as quickly as possible to reduce damage to your turret.
The turret starts by attacking the biggest/tankiest minion.
Switch focus, as the turret kills your minions one by once so you dont loose farm.
If you can, time it well, so that 1-2 enemy minions are still at your turret when your reinforcements arrive. But make sure to kill the enemy minions quick enough, so that the enemy minions do not reach your turret before your minions can step a little out. This way your minions will be blocked shortly and you will gather another freeze in your favour.
¶ creating a slowpush
This is usually a quick and effective move for objectives and teamfights.
suppose, its later in the game, there is some minion farm on the bottom or top lane.
-> Kill the enemy minions but make sure that your side does not have too much more minions. 1-2 minions more on your side max. Basically the opposite of maintaining a freeze:
Leave the lane right away.
More and more minions will gather there. But as your side has slightly more minions, your side will kill the enemy minions faster and faster.
More and more Minions gather, until a big army marches towards the enemy turret. Time it well, before baron or a teamfight. The enemy has to react now: send someone there or loose a ton of farm, maybe even the turret. usually 1-2 slowpushes which are not answered by the enemy fell a full health inner turret (the second one on the lane).
¶ Combining strategies (Denying Farm)
From Master on, you will usually see that these strategies are used in devastating ways.
When you relaize, that you are ahead of your enemy. Or your enemy is a closed combat, scaling champion (such as kayle) start by initiating a freeze. But you place yourself between your Minions and the enemy champion. (me, kayle is the enemy in this case) Keep the enemy away from gold and experience.
Doing that, you automatically initiate a slow push, since the enemy cant attack the minions, but you last hit them. With practice, you can even initiate a full freeze still, denying the enemy entirely from farm. Be aware, that this begs for 4 man squad ganks on your lane!
Anyways. You gather more and more minions. They will automatically start overwhelming the enemy minions and push towards the enemy turret. This is the physics law of mass and momentum. However, you try to stretch the timing of this as long as possible. A huge Minion wave deals as much Damage as 1-2 champions. Especially early on.
You guide your minion army into the enemy turret. Allowing you to take jungle farm, take the top tower thing, in the alcove, heal, go back or gank another lane. Should the enemy be so stupid to attack you solo within your minion army, take the free kill.
rince and repeat.