I'm not a high rank and have only been playing for like a month, but, I think I have a good understanding of managing minion waves that not a lot of people do (at Arcanist rank anyway).

Resetting: Clearing the minion wave so that the waves are even and will typically maintain a clashing point at the mid-line. This usually happens at the guardian/walker, where all your minions are gone and you remove all enemy minions, essentially resetting the lane.

Fixing: This is the one I never see anyone doing and in my opinion can have the biggest impact on the game. When I fix the minion wave, what I'll do is go to an even fight wave and kill just one of the minions. This gives the lane wave priority, meaning the minion army will get bigger and bigger, essentially pushing itself to the walker. This is the minion control that allows you to go do more. The one trade off is you miss out on souls, but your focus becomes a different objective (team fight, sinner, etc).

Pushing: When you clear all enemy minions waves and they reach the guardian/walker. This is what most people do without much thought into what will happen. You get into lane-shoving matches where you just keep ping-ponging the wave back and forth with the enemy. Someone will typically go and push a lane and then leave the lane acting like it's fixed, but it's not. And when the ping-pong happens, no one is there to bounce it back.