Welcome Summoners, to my first build for Poppy, The Iron Ambassador. In this build I will explain a bit on how to play probably what I have found for me, to be a very excellent build. I would like to remind you to at least try the build before you give it a vote and without any further a due. Let us proceed with creating an AP Carry Poppy that will deal and leave, A Devastating Blow.

Poppy has many Pro's and quite a few Con's, here they are.

Pro's:
Very good damage
Very good at escaping
Not very hard to learn and/or play
Skills give very good survivability
Quite Tanky Mid to Late Game

Con's:
Quite squishy early game
Take's some skill to understand how to farm
Take's some skill on understanding how/when to use ultimate
And can take some skill to learn how to play overall

For you skills you definitely want to max your Q first while maxing your E afterwards and still getting some points into your E and picking up R whenever you can.
The reason you want to build your skills in this way is because your Q is so devastating and does so much goddam damage any point in the game, that this will always be your follow up after you get your E.
Team Work:
However Poppy's best combo is her W->R->E->Q. What you want to do is W to be able to ambush your opponent however R right before u attack the enemy champion then try your hardest to E them into a wall which will stun them for 1 second and then Q them. However if you still don't have the kill and no-one else is around definitely use your Ignite and if able continue to chase. By the time this combo is done all of your skills besides your R should be back up allowing you to most likely get the kill.

Not much to explain here. I just get Flash because I find it to be so much better since your W already grants your a "Mini Ghost" in which case if you can't get away with your W you can pop Flash to get away. Ignite is just in case you need to finish up.

To farm with poppy what you want to do is only use your Auto attack or your Q. After using Q and after it's initial blow. You do more damage for about 2 seconds. This allows you to do an insane amount of damage to minions allowing you to farm quite effectively.

For rune's since you happen to be building an AP carry Poppy, you want as much extra AP as you can while also having some Armor just for extra survivability. If you have all the AP Quints, Blues, and Reds you will probably 60% of the time be able to get first blood at Lv.2 if you have your ignite up which you should because you should never go for a kill at Lv.1 unless you have an amazing tank that you trust whole-heartedly in lane with you.

For Masteries I usually build 21/0/9 however 9/0/21 is also another viable option. like I said in the Runes chapter, you want as much AP and damage as you think you need just so that whenever you hit someone with your Q you deal an insane amount of damage. Because of this you build 3 in Archmage's Savvy, Brute Force, Lethality, and Havoc. The reason you get 9 in utility or 21 Health/Mana regeneration which allows you to live a lot longer.
But, an alternative is 21/9/0 or 9/21/0 because as I said you want to be able to live whenever u go in for the kill, however, damage is definitely priority these are just other options.

Firstly go for your Sheen, then go for your Merc treads this'll give you some MR while also giving you some Damage. Then start building your Randuins Omen followed by your Force of Nature this gives you some more Health Regen and some more MR. Finish building your Trinity Force just because it gives most of the things I like to build on Poppy. Then go for Madreds because of the Health and Passive and if you make it this far you can start building your rabadons and if finished, you get a pretty ridiculous amount of AP. If this build is finished you'll have some MR, AP, and a great amount of HP Regen.

Basically in this build what you want to do is just help your team. You'll probably most of the time get an assist but just remember, E the person into the wall or ambush them with your W and R and then Q them for the massive damage. Remember your Poppy not Alistar, YOU ARE NOT a tank, don't just run in because you believe your a bad *** even though... you are.

And thank you to FinalFan for helping me realize a lot of faults with the items and the Runes. He's part of the reason this build is so much beastier.