Something nobody has mentioned yet is keybindings. (more specifically, smartcasting) If (during a game) you go into the menu and click on keybindings, you'll be able to change what keys perform what actions. More specifically, what keys are the "smart cast" keys. What is smart cast, you ask? Well, you know how Karthus' Q, Ez's archane shift, flash (and some other abilities), you need only use the key and it is automatically targeted at the cursor? That is smart cast. You can make any ability smart cast (though I've not tried with abilities like Rumble's Ultimate, Victor's death lazer, Varus' snipe, or other awkward ones). Having your abilities smart cast saves you fractions of a second for clicking, however, you will not see the "skillshot arrow" or the "aoe field". This can cause a lack of accuracy, so I only reccomend using smart cast (switching all of the smart cast keys to Q, W, E, and R) on appropriate champions (I never use it on Lux or Xerath, I use full smart cast on Evelynn and Ryze, and I use half smart cast for Nocturn). Ahri's combo (charm into ball) is a common smart cast scenario. I don't know if her dash requires a click, but I would certainly have that one be smart cast as well.
Hope my advice helpped.