This Technique called Wave or Waving is not really much considered here on LoL and i think it's not even known by most of the players, that's why i'm going to talk about it.
Waving takes a big part in Lane Phase Harassment, if you really care to win your lane and rise your elo, or you just want to win, Wave is what you need to know to Destroy your enemy.

Here's a little image that explains Wave



In few Words, Waving consists in AutoAttacking Before every Skill you are going to do.
Increasing your Damage and Optimizing Dead Times such: Cooldowns and Attack Speed.




Considerations:
Keep as example Renekton, Imagine that you are playing this champion.
Normally without knowing what is Waving if you would harass an enemy, your combo would be:

Without Waving
Combo
Slice and Dice + Ruthless Predator + Cull the Meek + Slice and Dice
Damage
Slice and Dice + Ruthless Predator + Cull the Meek + Slice and Dice
All your damage will be based on your skill's damage, but now let's have a look with Waving

With Waving
Combo
Slice and Dice + AutoHit + Ruthless Predator + AutoHit + Cull the Meek + AutoHit + Slice and Dice
Damage
Slice and Dice + Ruthless Predator + Cull the Meek + Slice and Dice + 3 AutoHit .
That could seem all not important but if you think that a Solo Top player or generally every Physical Champion starts with something like 80 AD's at Level 1 you would deal:
3 AutoHit X 80 Dmg = 240 free Damage
only because you are Waving.
(All excludes Armor, ok, but just think that Waving Damage is Incremented also by Levels and Items)

Champions that Can Wave
(every champion can wave but some better than others)
Akali - Annie - Blitzcrank - Corki - Darius - Ezreal - Fizz - Irelia - Jarvan IV - Jax - Kennen - Lee Sin - Leona - Lux - Nasus - Nidalee - Olaf - Pantheon - Renekton - Riven - Shen - Talon - Twisted Fate - Urgot - Vayne - Veigar - Vladimir - Volibear - Warwick - Wukong - Yorick - Ziggs


So, Will you Start WaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaving?