Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Farm and last hit, it procs your passive which regains your health and mana. This is why you get a mana potion not a health potion, as you use up your mana faster than health and health is regain faster. Use your abilities sparingly as spamming can lead to mana starvation. You need a lot of build so try to last hit as much as you can for that too. Try to get your treads and catalyst quickly.
Mid game: Feast on minions and on creeps to get blue buff as quickly and as many times as you can. Don't try to feast on enemy chamipions until you have 6 stacks. By this time in the game you can start tanking if you have treads, catalyst/Banshee's veil and Frozen heart. Still now you can start running all over the map to clear minion lines with your Rupture and Feral Scream combo.
Late game: You have 6 stacks, Doran's ring,Mercury's treads, Banshee's Veil, Frozen heart, Abyssal Scepter, and Guardian angel. Now it's impossible to die unless at least 4 of them focus you. Getting the blue buff will also help as you can spam your abilities while being unkillable making them run from you like crazy chimps. Lastly, if you still haven't won yet by manpiling turrets, then get all the elixirs and baron's buff for fun. You will have so many auras around you you'll literally look like a God.