Poppy is a very tanky champion that when built full tank can output considerable damage and in many cases solo kill squishies. Poppy can be played in an offensive or defensive playstyle, although she is better on defense. Poppy can be thought of as a meat shield that can itemize well against AD or AP threats, although Poppy does slightly better against AD threats. Poppy can be played in the Top lane, as a Jungler, and while not as optimal as the previous two positions she can be played as a tank defensive support. Best of all, you can blind pick Poppy and go neutral in just about any matchup, and Poppy doesn't need a large amount of gold to be effective so shutting down a Poppy isn't as possible as say shutting down a Renekton or damage threat like Yasuo. This guide is here to help you understand why certain runes,items, and masteries are good on this specific champion.

R>Q>W>E

I prefer to max Q because that is Poppy's primary damage, wave manipulation.

I prefer to max W, most people max E before W, because I prefer to have the stronger move speed buff instead of the 0.5 seconds extra stun time and the increased damage on Poppy's E. If you want to max E before W go ahead, I just prefer to max W so I can use the move speed to make more plays and dodge more situations.

I prefer a setup relying on Resolve with points in Inspiration to have more utility. My Poppy build isn't designed to hard split push or be getting the majority of kills so I don't use Precision or Domination trees. Poppy comes with enough base damage, you don't need to build much more damage to be effective. I don't use the Sorcery tree as I'm not convinced Poppy's kit works well with it.

Resolve Tree
Tier 1: Grasp of the Undying makes you stronger in laning phase and is an overall useful Rune with Poppy's playstyle of engage. Since you don't case spells on allies I don't take Guardian. I think Poppy does enough damage to champions so I don't get Aftershock

Tier 2: I don't personally like Demolish on Poppy. I prefer the extra tenacity that comes with Unflinching, especially after you Teleport and Flash on top of a target.

Tier 3: Conditioning gives you both armor and magic resist, after 10 minutes. While Iron Skin and Mirror Shield give you immediate stats, I prefer Conditioning into blind matchups and for its late game potential. If you know who your opponent is and think you will struggle, take either Iron Skin or Mirror Shield strategically

Tier 4: Overgrowth isn't very impressive. If you have a team comp that has a high amount of healing then Revitalize is a great Rune. Second Wind can help you if it is required to skirmish often. I prefer Second Wind to help give a slight sustain advantage in lane.

Inspiration Tree
Tier 1: Future's Market: There may be situations when you fall behind and need to keep up in items. Being able to deficit spend can help you get the item you need, get past the rough spot in the game and be relevant in teamfights.

Tier 2: Cosmic Insight offers CDR, a great stat overall. It offers CDR on your summoner spells, very important for Teleport Flash engages, and makes item active come up more often, great with multiple items Poppy loves.

Pros

1: Does lots of damage to champions with base values
2: Can work well with almost any tank item
3: great defensive champion
4: Can be an offensive champion
5: Has build in 15% bonus resistances, a move speed buff, and small wave manipulation
6: Can be blind picked into just about any top lane and is a proficient Jungler. technically can support, but it's not optimal.

Cons
1: Has a mana problem due to constant need to Hammer Shock
2: Is Flash reliant for engages
3: Needs some help with weak base kit wave manipulation.
4: Heroic Charge has a "wonky" hit box and requires practice to hit many different stun angles
5: You have to be ready to Teleport at a moments notice... if you are late on TPs you are useless to team.

My Standard build for Poppy is Bami's Cinder -> Iceborn Gauntlet -> Mercury's Treads -> Guardian Angel -> Dead Man's Plate + Situational item.
This build, with flat Armor and Magic Resist runes, gives: 3120 HP, 387 armor, 429 Move speed (including Dead Man's Plate bonus), and 177 Magic resist at level 18. This right here is a very beefy Poppy, leaving you room for a 6th item of your choice. Note, this build is made with the assumption the team is running a standard AD Carry + AP Carry + Mostly physical threats and I can just ignore the support damage.

Corrupting Potion: due to Poppy using/needing Hammer Shock for trades and any kind of wave manipulation Poppy has a little bit of a mana problem. Until we can get a full Iceborn Gauntlet this should help alleviate the burden.

Iceborn Gauntlet: gives much needed 20% CDR, much needed mana, much appreciated armor, and an AOE slow. The only reason that I wouldn't buy this item is if the enemy team has absolutely no attack damage threat.

Sunfire Aegis: Gives strong HP, good armor, and the AOE burn helps with wave manipulation and teamfight damage. The only way I don't build this item early is if there is no AD threat on the enemy team.

Ninja Tabi: Are you facing an ALL AD team? If yes, buy these boots. If the answer is no and they have a magic damage threat or they have lots of hard hitting CC then don't buy these.

Boots of Swiftness vs Mercury's Treads: If the enemy team has high magic damage and hard crowd control, then pick up Mercury's Treads. If the enemy team has lots of SLOWS, but not necessarily hard hitting crowd control, then buy Boots of Swiftness. I usually prefer Mercury's Treads so i can buy M Treads + Guardian Angel and have plenty of magic resist so I can buy pass having to buy an early Banshee's Veil.

Guardian Angel: this item makes you a PAIN IN THE *** to kill, and it gives you much appreciated/relevant resistances. I love getting this item 3rd after I. Gauntlet and S. Cape

Dead Man's Plate: This item gives Poppy map roaming potential, that's about it and that's an extremely important commodity.

Warmog's Armor: A great 6th item to compliment your heavy resistance builds. Can be bought late in many circumstances, but against all AP teams (think ARAM or unusual troll games) you can think of this as a first major purchase.

Sightstone -> Ruby Sightstone: If no one on your team is picking up the slack on vision control then you may have to suck up your pride and put this item on.

eye of the equinox: I rush this as a support to streamline my tank support build and make room for more tanky items.

Turbo Chemtank: want to run fast? Want a little bit more mana? If yes, then this item will work for you. Warning, no resistances come with this item and it sets you back from becoming a truly unkillable tank, but this item is fun.

Zz'Rot Portal: This is a cool item that can be used to help you apply pressure to a side lane, or help you defensively hold onto an inner turret. The big idea around this item is to coordinate with your team to make sure that while the portal is up you are on the other side of the map helping with teamfights.

Zeke's Harbinger: While the AP is a waste on Poppy you buy this item with the intent on slapping on one of your carries, preferably the ADC however if you have a consistent AP threat( Ryze, Casseopia, Azir, etc) then chose one and help that person snowball harder and do more damage. This item isn't really good in the 1-5 slot but it makes a decent 6th item.

Thornmail: I usually don't buy this, mainly because most other items offer some better tank or utility options, but if you are against a full AD team this item will round you out to be 99% indestructible.

Randuin's Omen: does the enemy team have a crit heavy threat that is becoming hard to deal with? If yes, buy this item. If not, you don't necessarily need this item because other armor items offer better utility.

Knight's Vow: an interesting option, kind of using the mentality behind buying F.O.T.Mountain, I wouldn't buy this early due to the low "individual" stats wouldn't be great for laning phase. While in theory this item would be better for the 2 of you to stay alive, if you are against more burst oriented champions, cough cough assassin meta, then I don't think this item is good enough. It's ok, but I prefer the on command press of F.O.T.Mountain as a 6th item to keep my squishy alive.

Frozen Heart: does the enemy team have a damage threat that is based on auto attacking and needs high attack speed (Kog Maw, Vayne, xin xao, Yasuo, etc). If yes, this item is perfect for your team.

Locket of the Iron Solari: This is a cheap item powerspike that gives your team a temporary shield. Not a good early purchase for a top laner, I think they need to be more rock solid, but as a 6th choice to protect your team with a strong shield, it's good.

Talisman of Ascension: this is more of an ARAM strat, but you buy this item so you can still have gold gen and help start fights. It also comes with armor so pretty good bang for a 2400 dollar buck. It is fun to buy this as a 6th item in top lane, just not a dependable top lane item. Please don't buy this early in top lane, seen some people do it recently, it doesn't go well for them.

Banner of Command: gives Armor + Magic resist + more split pushing/side wave management. An possible strat is to buy Zz'Rot and Banner of Command back to back and have the top lane perma push, and coordinate this with your team so you can prepare elsewhere on the map. This can help you make cross map plays and save Teleport.

Banshee's Veil: if I need a magic resist item NOW I go to this item. it's cheap, it has high magic resist, the unique passive (blocks one spell) arguably make it one of the most rock solid tank items in the game and magic damage gets shut down. Very effective item.

Spirit Visage: I almost never buy this item. It's more expensive than B. Veil, it has less magic resist, I can get CDR from other items, Poppy doesn't have any champion specific health regen modifiers so the unique passive on this item is kind of useless. As a 6th item if I'm against a consistent AP threat that is causing me problems then I add it to my standard build. If I am against an all AP threat I pick this up after Warmog's Armor and Banshee's Veil.

Maw of Malmortius: This is a more offensive option, it either goes as as 6th item in a standard build against AP threats if I'm feeling more confident or you can build this early against an AP threat if against an AP team.

Mercurial Scimitar: similar line of thinking that I used with M.O.Malmortious, except this item comes with an on command "cleanse" which can be really powerful.

Edge of Night: Similar line of thinking to M.O. Malmortious except this item can be paired with B.Veil, with strategic timing you can negate 2 spells when trying to engage and be less likely to fail.

Tiamat -> Titanic Hydra: In a standard game there is no reason to buy this. I. Gauntlet + S. Cape fix your wave manipulation problem. However if you play on Summoner's Rift and find yourself against 5 AP treats then you can't rely on on these items to fix your problems. Since there aren't any good mana items that go along with magic resist you have to work around Poppy's need for mana and I chose to buy a Tiamat and later on turn it into a T. Hydra so I still have damage and wave control.

Black Cleaver: If you want more damage, this item offers armor shread (useful for the whole team) and it helps you stick to your targets.

Trinity Force: due to how cost effective, and just how effective, Iceborn Gauntlet is you will/should almost never buy this item. However, if you find yourself snowballing the game early then go on ahead and buy this item, I would be lying to you if I told you it wasn't fun.