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.
Short n Sweet
Doran's ring for early health boost, mana regen and ap boost (for passive and abilities)
As soon as I can afford the first philo stone I'll B and use teleport to get back quickly. Again will go back once I can afford boots and another philo stone. The 2 philo stones give you nearly unlimited use of your abilities. Addionally, the gold per 5 on the 2 stones makes your subsequent items come much quicker. However, you do delay your burst game by 5-7 minutes. It'll catch up in the long run though.
Sheen and sorc boots give you a nice autoattack boost as well as some magic pen to go along with your abilities and passive damage. Also allows you to take down towers faster. Simply spam q while autoattacking the tower.
Catalyst/Rod of Ages is self explanatory. The nashor's nearly caps out your CDR along with the masteries (39%) as well as giving you a nice autoattack dps damage/speed boost.
Rylai's for more survivability along with the slow and damage boost.
Rabadon's makes you hit like a truck. ~200 ap boost gives your autoattacks +40>70>100>130 extra damage.
Lichbane rounds it off nicely. With the full build, I am able to hit the inner towers for ~800 using lichbane effect, and the nexus for ~1000