Poppy is, when well played and at most cases one of the best assassins on the League. People who have seen a builded Poppy rapidly complain about her and SCREAM for a nerf.

But that Legendary Poppy is never nerfed well, because it is almost never seen.

When a summoner tries to pick Poppy the team rages and he's convinced he'll do good because he's seen some play where Poppy did a really nice score. Well, he will face the cons and never get to the pros until a lot of games later, with luck.

POPPY CAN'T FARM and that's why she's left behind on the champ select. If you manage to get to late game you will be flawless but if your opponent is not reaaaally bad, you won't have the chances to get that far.

THAT'S WHAT THIS GUIDE IS ABOUT

Poppy getting all the money she couldn't get on most of the plays, making our opponent think he's gaining lane when what he's doing is lose money. We will get SAFE to late game, maybe get one or two kills in the way and them COME IN LIKE A WRECKING BALL.

Aw, that cutie yordle. She's my little girl.

Well, the support changes opened the gates.
Turns out that ancient coin:
Gives us not only the power to gain gold even if we can't last hit (really an issue when you can't spam the q as much as you need it, but also a lovely sustain in line thanks to life regen. That, combined to our masteries (full sustain), will help us stay safe and collect farm all the early game, while building calmly and neverminding about our opponent.
If he hits you and gets away, you got life regen. If he stays, you hit him harder with your hammer and break his neck. Back then and keep farming, he will jump on you less often.
When he does that, have your W prepared, cause it's the better way to have him asking WHY THE HECK YOU LAST THAT LONG.

Well, we will max up that w to use that lovely sustain, and we will keep on shopping, finishing our Talisman of ascension:
...And gaining a 20% Cooldown Reduction to spam the q as long as we want.

The other thing I buy (BECAUSE YOU CAN CAN CAN), usually after finishing the Talisman, is Avarice Blade. It gives you gold per second and has interesting posibilities once you finish it.

You don't really need that masteries, since your runes and build will still be prepared to do dammage. What I like to do with her is buy her some hybrid burster sh*t: Nashor's Tooth to charge the autoattacks; Lichbane, to max the next attack following the q; and maybe Guinsoo for the pasive which I never actually buy.

She will become a killer the second you finish your W and start hitting hard on the Q. Remember your objective to face with the ulti will be more important than focusing the rest of the team with this build. You're meant to KILL THE TANK! not to run away from a teamfight or kill the support.

Once you build her correctly, landing the E and using the ult is easy once you practice enough.

Enjoy playing Poppy, tell Riot she doesn't need to lose that ult or passive (Morello already commented about it, he's planning to change everything except the E).

And don't waste that well earned money.