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.
Poppy is quite a fun character to play, you can one on one most people and chase people like no tomorrow. Most of the high rated guides I've seen are ad/as but ap performs just as well!
The sequence you want to use is E > Q > W then repeat. Most of the time you won't need R, but if you do, I'd stick in in there before Q since you'll already be in range. Doing this rotation, you will get the most of the Lich Bane/Sheen procs.