How the game behaves, in plain words.
Minion waves
Minion waves leave each base every 30 seconds and meet in the lane. Most of your early gold comes from last-hitting them, landing the killing blow on a minion. Where the waves meet decides who is safe: the closer to your tower, the safer you are, and the further your opponent has to walk to reach you.
Crashing the wave
Crashing, or fast-pushing, means clearing the wave quickly so it reaches the enemy tower. While the tower kills it you have a free moment: back, ward, or help a fight. The wave then bounces back towards you, so the best moment to back is right after a crash.
Measured below: Shop visits before 14:00.
Roaming
Mid is the shortest lane, so a mid laner can reach a side lane quickly. Roam after you crash your wave into their tower, so you lose little, and come back before the next wave reaches your tower.
Minion aggro
If you hit an enemy champion with an attack or a spell while you are near their minions, those minions switch to attacking you for a few seconds. Trading next to a bigger enemy wave costs you extra health, so trade when the enemy wave is small or your own wave is bigger. Enemy towers do the same: hitting a champion under their tower makes the tower target you.
When to back
Back when it costs the least: right after your wave crashes into their tower, when you have the gold for an item or component that changes a fight, or before an objective your team is going to contest. Backing with a big wave about to hit your tower loses minions and tower plates.
Measured below: First trip to the shop, Gold in hand then, Shop visits before 14:00.
Power spikes
A power spike is a moment your champion gets much stronger: levels 2, 3 and 6 (your ultimate), and each finished item. Fight when you have just spiked and your opponent hasn't, and avoid fights just before theirs. The matchup section of your game review in the companion shows the levels your lane opponent usually gets kills at.
Vision
Wards show you where enemies are; a control ward also reveals and disables enemy wards near it. Ward the river or the enemy jungle entrance before you push forward, and place a control ward where you will fight later. Your trinket recharges, so use it whenever it is ready.
Measured below: Wards before 14:00, Control wards before 14:00, Wards a minute.
Objectives
Dragons, Void Grubs, the Rift Herald and Baron give your whole team gold or power. Push your wave, back and buy before they spawn so you arrive first with full health. A team that arrives late, with waves crashing into its towers, loses the objective and the plates.
Measured below: With 2+ teammates from 20:00.