Hello, my name is NyanH3ro, i am a Silver V (and climbing) Ezreal main on OCE who likes to play stupid or non meta builds, i hate solo queue and enjoy playing in groups of 2-5. I have been playing league for a few years and i have enjoyed almost every game i have played. I generally don't care whether i win or lose, as long as i have fun.

This is one of my first guides and I have probably made mistakes, please excuse these.

Pros

-Very high damage.
-Can peel and protect allies really well.
-Her ultimate Keeper's Verdict can win games if you aim it right.
-Can counter jumps.
-She is a yordle.

Cons

-Can be poked down easily
-Requires you to land your ultimate correctly
-Need good reaction time to use your W Steadfast Presence if an opponent with a leap engages. (for example a Rengar)
-No resistance against short jokes

Here is a list of Poppy's base stats at level 1, and level 18

Health
Health at level 1 - 540
Health at level 18 - 2070

Health Regen
Health Regen/5 at level 1 - 8
Health Regen/5 at level 18 - 21.6

Mana
Mana at level 1 - 280
Mana at level 18 - 960

Mana Regen
Mana Regen/5 at level 1 - 7
Mana Regen/5 at level 18 - 18.9

Attack Damage
Attack Damage at level 1 - 56
Attack Damage at level 18 - 124

Armor
Armor at level 1 - 29
Armor at level 18 - 88.5

Magic Resist
Magic Resist at level 1 - 32
Magic Resist at level 18 - 53.3

Movement Speed
Movement Speed - 340

Passive - Iron Ambassador

Iron Ambassador - This is your primary skill for early level's, use it to poke the enemy down and farm. also remember that if you are in melee range when you throw your shield it will reset your auto.

Important Note: Iron Ambassador is treated as a melee attack, and thus procs all melee on hit effects, and will not proc any ranged on hit effects.

Damage - 20-190 base damage as Magic based on your level.

Q - Hammer Shock

Hammer Shock - This is what makes Poppy the beast that she is, it deals decent base damage, and has decent AD scaling, plus it deals 6% of the enemies max health, but it deals 20% less damage to minions. The low cooldown and mana cost means that you can spam it to farm as much as you want (just don't go too crazy and waste your mana).

Damage - 30/65/100/135/170 base damage + 0.65 per bonus attack damage + 6% of the targets max health as Physical Damage.

W - Steadfast Presence

Steadfast Presence - Activate this ability to disable all dashes/leaps around you (only once per champion) and for a burst of movespeed, also increases your armor and magic resistance by 12%, increasing to 24% when you are below 40% health.

Damage - 70/110/150/190/230 base damage + 70% of Ability Power as Magic Damage.

E - Heroic Charge

Heroic Charge - At 40% cdr this becomes a 2 second stun on a 4.8 second cooldown, which means that after the stun ends your opponent will have only 2.8 seconds to flee. Just remember to hit a wall with this ability, otherwise it will not stun.
Damage - 50/70/90/110/130 base damage + 0.5 per bonus Attack Damage as Physical Damage.

R - Keeper's Verdict

Keeper's Verdict - Can remove high priority targets from a fight, or save your team mate from that low health enemy, who was obviously about to turn around and kill him, they will thank you for this by saying 'wtf', which means 'Wow thankyou friend'.

Damage - 200/300/400 base damage + 0.9 per bonus Attack Damage as Physical Damage.

Marks

Greater Mark of Attack Damage - Most of Poppy's abilities scale off bonus AD, this helps with harassing with your passive and your all in damage.
Greater Mark of Critical Chance - The infamous 1% crit chance rune.
greater mark of armor penetration - For extra penetration.
Greater Mark of Attack Speed - I guess why not.

Seals

Greater Seal of Armor - Standard 9 armor helps alot against auto harass in lane.
Greater Seal of Scaling Health - If you don't need the armor then take these.
Greater Seal of Scaling Armor - Scales the passive on your W, Steadfast Presence, more at late game, at the cost of being more vulnerable at early levels.

Glyphs

Greater Glyph of Scaling Magic Resist - Since AP champions do alot more late game then they do early game these runes will help you against their scaling.
Greater Glyph of Magic Resist - Flat magic resist, helps more early game, but drops off late game.

Quints

Greater Quintessence of Attack Damage - Same reason as the marks.
greater quintessence of armor penetration - Same reason as the marks.
Greater Quintessence of Attack Speed - Same... reason? As the marks?
Greater Quintessence of Scaling Armor - Better scaling on Steadfast Presence late game.
Greater Quintessence of Scaling Magic Resist - Better scaling on Steadfast Presence late game.

Starting Items

Corrupting Potion - Gives you a good amount of sustain in lane, you will start with this most of the time.
Long Sword - Gives you a decent amount of damage, you will start with this if you want to trade and play aggressive.

1st Item

Ravenous Hydra - Gives alot of damage plus the active is like a 5th ability, the lifesteal is really good and it makes wave clearing alot easier. This will be you standard pickup, altho you can switch it out for Titanic Hydra at late game for more health.
Youmuu's Ghostblade - Gives decent AD and armor pen and 10% cdr, the active is great for dueling, chasing, escaping. If you buy this then then you will be unable to buy Ionian Boots of Lucidity and Iceborn Gauntlet due to over-stacking cdr.
Frozen Mallet - Not much to say about it, it gives you 40 AD and alot of health, as well as a slow on hit which applies to your passive Iron Ambassador.
Blade of the Ruined King - The %health damage on this item is decent, and the attack speed will help in alot of situations. More of a situational pick than Youmuu's Ghostblade.

Core Items

Black Cleaver - standard item on Poppy, her Q Hammer Shock, procs it twice. It gives a good amount of health and AD as well as a glorious 20% cdr.
Rapid Firecannon - It increases your passive Iron Ambassador range by 150, making it a long range poke ability. you can sub this out for Statikk Shiv if you don't want the range from rapid fire.

Boots

Ionian Boots of Lucidity - 10% cdr on abilities and summoner spells, which general 10-20 seconds depending on your summoner spells (have yet to test how much you they are reduced by). Build this if you haven't built a Youmuu's Ghostblade, and don't plan to buy Iceborn Gauntlet.
][mercury's treads]] - Build this for magic resist and tenacity.
Ninja Tabi - Build this for armor and auto attack damage reduction.

5th Item

Trinity Force - Scales really good off base AD, and Poppy has a pretty high base AD of 124 (which is higher than most), and 155 base AD with Sterak's Gage. This adds upto 248 bonus damage on Trinity Force without Sterak's Gage, and 310 with it.
Iceborn Gauntlet - 20% cdr, 65 armor, 500 mana, and a slowing effect in exchange for less damage. A decent pickup if you team lacks many tanks. (2 or less)

Final Item

Sterak's Gage - Increases your base AD by 25%, and increases your Trinity Force damage to 310, also gives a decent amount of health and the active can be really helpful in bad situations. For more of a tanky end build.
Infinity Edge - Gives you 20% crit chance for a total of 50% crit chance, also increases your critical damage to 250%. the 65 AD on it also increases your damage from auto attacks and skills. For more of a bursty end build.

some basic Poppy combos in lane are:

[Vs a dash champion]
if E doesn't hit a wall: E - W - AA - Q
If E hits a wall: E - Q - W - AA

[not Vs a dash champion]
If E doesn't hit a wall: E - AA - Q - W
If E hits a wall: E - Q - AA - W - AA

I will be updating this guide when i have spare time, i will be adding proper matchups, item explanation, laning tips, grammar corrections etc. It may take awhile to do each segment.

I am currently in the process of rebrainstorming this build due to buffs/nerfs to items, it will take time to find out what works.