Kiting/Orb Walking/Moving While Autoing
So most people already know that move you can in between your auto attacks. This is a really important technique in League, especially for ranged carries because it allows you to kite your opponent or chase them while continuing to apply damage. What many people don't seem to know, however, is that this technique also applies to melee champions!
There is an animation that each champion must complete after auto attacking that can be interrupted by a movement command. If you practice a bit, you can learn exactly when the damage from your auto attack is applied and move immediately after, canceling the rest of the attack animation. This is most noticeable on champions like Riven (who is known for her animation cancelling) but really you can do it on any champion. This skill is incredibly important on melee champions, especially those who rely on sustained auto damage such as Udyr or those who have auto attack passives such as Diana because it allows you to continually apply damage on a target that is trying to run away from you, or it allows you to retreat back while still fighting back.
You should never ever just click on someone and let your character auto path for you. It will increase your damage (and decrease the damage you take) by a significant amount if you master this little trick. It also makes it much more difficult for your opponent to land skillshots on you if you are constantly moving. Just be careful, because it is very easy to accidentally cancel the damage from your auto attack which can lose fights for you!
I understand that this seems like a very basic tip to many of you. Personally I used to think it was common sense, but in many of the games I've played recently I've seen a ton of people who do not move in between their auto attacks both on melee as well as ranged champions so I felt it was worth mentioning.