How do ADC's aa and move and aa so fast!?

You can do it with any champ.

Every autoattack has a "windup " animation. Before the hit, and a wind down after. Take Garen, for instance. He heaves his sword, swings, then waits a second before swinging again. That wind down animation can be cancelled with a move command.

There is an attack move command in league. It's essentially "move here, but if anything is in range of an attack, then attack it." The fastest way to attack cancel, especially for AD carries, is to bind attack move to middle mouse button, then regular move to right mouse. So what you do is just click where you want to go. Middle mouse, your champion attacks. Right mouse, same spot , your champion moves.

attack move-cancel move-attack move-cancel move. Etc.

shift button op or click fast

Atack move and animation cancelling.

Build Runaans+Berserkers' Greaves. Problem solved. (Unless you're )

Practice and timing grasshopper...

just start auto ing then moving it doesnt have to fast at the start and naturally you will do it out of habit and then you start doing it fast out of habit just let it happen i learned to stutter step with kog maw and i dont even play adc voluntarily i only do it because it's good to have the ability to fill now that i know how to adc i have only lost 2 games as kog maw

It is called kiting, or animation canceling. They do it through a LOT of practice. Basically you use the attack move button (A Left click by default) in between using your standard move (Right click) in the direction you want to run. The attack move makes you stop and attack if anything comes within your AA range when you are moving towards the spot you click, and the regular move cancels the attack animation, meaning they can move extra far in between shots.