I've been playing Poppy for a very long time, and I tried a lot of different builds with different items, runes and masteries, and I found that this is the best way to get in the fray and kick some ***, you will be carrying hard most of the games, and the enemy team will say that Poppy is OP and a lot of stuff that will make you want to kiss my *** for showing you how to deliver hard and heavy with this midget that really thirst for blood. You will find that EVERY little thing, every point in the mastery tree, every item, every rune has a reason to be there, and they're all there to make you the biggest pain in the *** that the enemy team could ever have, so, let's get down to bussiness.

*This build works like crazy for DOMINION, se be sure to check it out in there too!!!

*Build Reworked! - Dedicated to Nek/Groovy/Tellmemoree, the true jungling Heimerdinger (TIRI-TI-TI TIRITI-TI!!!) and my good friend Freaakside/Pablovich; "A true crazy Poppy never goes to golem or lizard for buffs, she simply kills all the enemy champions that have those"

Pros:
+Probably the best nuke in the game.
+Puts on the hurt with both AD and AP
+Amazing movement speed.
+Incredible DPS and survability.
+Has a good CC.
+Great ganker.
+6 secs of invulnerability.
+Strong 1vs1 (not as good as say WW, but still pretty good)
+Very versatile champ.
+Great tower diver.
+Great chaser
+Amazing escape mechanism
+It's a freaking midget chick that can kick some serious ***. That's pretty humiliating!
+Fun champ!!!

Cons
-Weak early game
-Poor farming ability until mid-game
-Kind of squishy
-Vulnerable to CC
-Not an amazing pusher (not bad either)

The best ones would be Exhaust and Ghost , because of the synergy they have with your abilities and items, but maybe you feel more comfortable with other spells, you can take them of course, but maybe they won't fit as good as the ones I'm recommending you.
Ignite and Flash are also good choices too. Try different combinations and see what fits you best (anyway I think you'll end up with ghost and exhaust, but knock yourself out!)

Ok, There are some that are a must and others that you have a few options.

Regarding marks, there's no discuss that armpen are the best ones for a melee fighter. Period.

About quints, u have a few choices between armpen, crit chance or mov speed, but i find the latter really useful, cuase they help u with the harass early game, and remember that u should be building sheen even before boots, so these quints compensate your lack of speed while you're running without your W, and they also give a nice boost while you have Paragon. (Thanks to Taxadar for this suggestion about quints.)

For glyphs, the best ones are flat cdr, but u can get cdr per lvl, they work just fine. On the other hand, maybe u prefer to be a little bit beefier and go for magic resist glyphs, wich are excellent, both are great choices.

Finally, i choose attack speed seals cause they help me with the last hit in early game, but u can take armor, mana reg or health seals, feel free to match ur needs.

So, this build may seem a little bit odd, but I find it very accurate in terms of getting the job done, because of a simple reason: You're Poppy, ur job is to slam someone against a wall and get the kill in less than 3 seconds, if u fail to do that, then run around a bit till u can CC again, by all means, never stay in the fray unless you are absolutely sure that you are gonna survive.
We start with because Poppy is a little mana-starved, and it's one of the items u need to build , wich is all u need to kick *** till mid game. Sheen should be ur first item, because ur strongest feature is ur nuking capability, besides that, Poppy is a really weak champ early game, so try to play defensive and focus on ur farming, and if u see someone standing near a wall, by all means, slam that *** hard and nuke the hell out of it.
About boots, u have some options. I go with the magpen boots so I can have defense pentration in both my ad damage and my ap damage, wich is pretty cool, but if u feel u need those +35 tenacity, go ahead and take Mercury tread's cause the mag resist buff is nice too.
Another option would be to take , but I don't think that u need that much attack speed, trinity force and alacrity seals give u just enough, but if u really want them, their not a terrible choice. Any other pair of boots is purely situational, so these 3 would be ur best choices.
When u have Sheen and ur boots, u should consider finishing . This item has Poppy all over it, it gives u a little bit of everything, and that's just what u need, not to mention the boost to the passive of Sheen and the 25% slow chance. Really, Trinity Force just beats Lichbane in terms of Poppy, think about it. I've been told so many times that Poppy should always be built as an AP champ, but those build fail on Poppy, cause of the fact that poppy is a melee champ, that needs A LOT more than just AP, cause u have to get in the fray, u have to auto-attack ur enemies, and u just can't die if somebody throws a few spells at u. Building Poppy as a mage is a terrible decision, trust me, u can't farm, u can't tank, all u do is hit a bit more with ur Q and E and that's it, u're left hopeless and defenseles when u're waiting for ur cooldowns. Man, that just CAN'T happen, u're not a ranged char, for god's sake u don't even have a harass spell, u're a midget chick that whacks people with her hammer, and EVERY TIME that hammer hits somebody, it has to hurt, not just even 1 big blow and that's it. That's why u NEED AD, that's why u NEED attack speed and crit, maybe not much, but u have to have some, just as much as u need AP to hit with ur skills.
When u finish ur Trinity Force, I suggest u start working on ur defense a bit, because every Melee champ needs at least 1 defensive item, but, as we don't want to leave our offense behind, I think that buying and is the way to go, so u can always heal a bit while u're putting on the hurt, making u beefier. Remeber that with Spell Vamp, ur Q and E heal u, and u hit a LOT with Q and slammed E, so u'll be healing a lot also. That's why I feel that Hextech is just as perfect for Poppy as Trinity Force. A lot of AD, a lot of AP, and when u attack, either with spells or auto-attack, u get healed, not to mention it's active. Man, that slow is just TOO great, it guarantees the kill, AND, if u're having trouble landing ur ulti cause of a pesky on the enemy team, u can pop that **** off them with this baby, and it gets better, u can do this as soon as u have ur so u don't have to wait to have the full gunblade. Again, this item is just too good for Poppy to let it stay sitting on the shop, just waiting for a smart Poppy that'll buy it.
Before explaining why Gunblade is such a kickass item, I said something about building defense, so i'll take it from there. When u have ur healing items ready, consider buying a Negatron Cloack, just cause u have such a poor base mr that mages can hurt u a lot, and u have to take a few shots from time to time. U can even buy it before lifesteal and spell vamp if u want, but i feel that healing when u hit something is just too good. So, with that cloack, we'll be building another amazing item for Poppy, and that's . It gives Health, Mana (thx lord) and that incredible shield. If u think about it, this item could be better on Poppy that any other defense item, because of ur passive. Between Trinity force and banshee, u'll be somewhere around 2500 health at lvl 18, and that number is just perfect for Poppy, not more, not less. Why? cause ur passive activates if u're hurt for more than 10% of ur max health, and this means that if u have a lot of health, u're gonna need to get hit heavier to activate ur passive, so actually, u're more effective in terms of defense if u have average health, armor and mr, but u can reduce 50% of the damage from a lot of blows, than having a lot of mr, armor and health (thus no dps), but only reducing 50% damage from a really large nuke, cause that's what it'll take to hurt u for 10% of ur health. I didn't actually do the math, but it's plain logic.
So, u have ur Trinity force, ur boots, ur hextech and ur banshee... well usually it's GG but since u have 6 slots, let's make the most of them.
Moving on, the best choices now available for Poppy, are pretty obvious if u think in terms of DPS.
So, I guess u noticed that u have a lot of AD and AP, and you can do some serious *** whopping if u can grab someone, even if it's a tank, and u have really nice stats. All you need now is just more AD and AP, so u can heal even more, and hit harder, and be beefier. That being said, next 2 items are simply the best item available for an AD champ and the best item available for an AP champ, as plain as that, and those items are and .
Well, u're probably wondering "ok fine, but wich one first?" and the answer's easy: since u're crit chance with IE gets somewhere around 50% with Crit quints, u're not able to take full advantage from this item like say Tryndamere does, cause u're lacking some crit chance, so i think that u should leave IE for your last item, and build cause u already have like 110 AP, and rabadon gives u those whopping 140 AND the +30% passive, which makes ur AP get to a number near 320, and that's A LOT of AP. I can hear some of u thinking "well, but u're not taking full potential of rabadon either, cause a full AP build would do that" but, let me tell u my friend, u're forgetting about something very important here. I said earlier that trinity force, Hextech, Banshee and boots are just the perfect items for Poppy, and the 2 best possible choices left were the best item for an AP champ and the best for an AD champ, wich brings us back where we were before when I said that u should be building Rabadon's for your fifth item.
That being said, there's really no better combination of late game dps items for poppy, no plus IE, no IE plus , no IE plus , or any other combination that works on any other melee champ, or the mage version, being Rabadon's plus any other high AP item, no other combination of 2 dps items will work the way that Rabadon's and IE work on Poppy. Your Spells hurt like ****, your auto-attacks also hurt as ****, dealing something like 800 dmg on crits, and u get healed as **** either with your auto-attack and your spells.
Trust me, if u want DPS, no Xin Zhao or Tryndamere build, or any Leblanc, Brand, Annie or any other AP nuking build is going to synergize with your spells and be as effective in terms of both DPS AND survability as the one I'm proposing here. Poppy's a natural hybrid, tanky DPS, just like Jax, and her potential in this role is just as great as the latter.

Well, this is pretty straightforward, but there's a few changes u can make. There's no doubt that maxing ur first is what any poppy should do, but when u have finished with that, u have a few other optiones. First, think about whether u want to lvl up ur ulti every time u can or u just spend 1 point at lvl 6 and don't touch it until 17, it depends on ur play style, I tend to be pretty agressive, so I prefer to max right after Q cause it gives u armor, damage, and speed buff, so I can make better chases and escape hairy situations, but, if u love the burst damage of ur combo, then u should prioritize over W.

This is a very fun champ that it has a lot to offer if you give it a try. I've been playing her for quite a while now, and I have grown very fond of her. I got my ups and downs, I'm not gonna tell you that I own with her every time, but I found that with this build every item is there to boost every little aspect of her playstyle, and I think that's very important for every champ. I really hope that you find this guide very useful, and if you got some feedback please feel free to comment, I'll be glad to know how did this set-up worked for you, and we can discuss any idea that you came up with.
Have lots of fun!!!