My match history with this build
I don't take any credit for this guide and I have never written a guide before. I put this guide out because I haven't seen any other poppy guides on this website capitalize on how well 40% CDR works on Poppy and I find Shurelya's Reverie invaluable.

I have tried many builds but imo, there are none better than this because this is what poppy is.
You shouldn't have to base when your at 1/4 hp, stop it, and try this build.
Leave pure dps builds to other champions, poppy is tanky, and with this build you will not sacrifice much damage. Contrarily, your abilities will almost be up 100% of the time so you can spam your Q+E on someones face, and with Shurelya's Reverie + your W you are un-catchable or they are not getting away without dying.
My match history with this build

This guide is for the beginners who want to discover what Poppy is and how to, one day, learn to love her play-style. This guide also is for the Poppy lovers who want to hone on her abilities and skills to maximize her. I have played Poppy ever since she was available. Through time I have learned to love the character she is, and also to never underestimate her true power. This guide is not to show that I am the best Poppy out there, because I'm not, but to simply share the knowledge and passion that I have for this one character. I hope you enjoy! :)

RATE IT!: If you have read the whole guide and you like it, rate it up. Every little bit helps. Also leave comments on anything that I might of missed out on or suggestions. Thanks!

The first build is what this guide is focused on, CDR Poppy.

The second build is Crit Damage Poppy. The reason for crit damage is this:
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Crit Chance: 71.95%
Crit Damage: 310.61%
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The Crit Damage is good after a solid 70% Crit Chance. Now that we have achieved that through Items, we can easily glyph for Crit Damage runes. I will let you find out how hard your auto attack are hitting for at engame. :)
Strategy: The Crit Chance build will be tough early game, but by late game you will have your enemies feeling the pain. There is more survival in this build as you will not hit as hard as you would in the Nuke Poppy build, so stay back and push with your lane partner as you see fit. Also, make sure that you always stun the enemy with Heroic Charge. You will need to make sure that your enemy is stunned for the full duration so that your Crit Chances will do alot of damage.

The third build is Tank Poppy

The fourth build is AP Poppy Heres the numbers for this build:
Devastating Blow
Poppy crushes her opponent, dealing attack damage plus (+300 ability power) plus 20/40/60/80/100 and 8% of her target's maximum health bonus damage. The bonus damage deal cannot exceed 75/150/225/300/375.

So thats 526dmg +8% of the targets max health which cannot exceed 375. so you can do maximal 900dmg . Now its time to add the 100% bonus dmg from the lichbane passive after you cast DB, so it will be a 900 + 500 bonus dmg for 1400 dmg with one swing!

Heroic Charge
Poppy charges at an enemy and carries them for a short distance. The initial impact deals 50 / 75 / 100 / 125 / 150 (+200.025 ability power) magic damage. if they collide with terrain, her target takes 75 / 125 / 225 / 275 (+200.025 ability power) magic damage and will be stunned for 1.5 seconds.

so thats 825 dmg when you can charge them against a wall

So with your ulti up you have an dmg output from (1400 + 560 from your ulti)+8% enemy max hp with your DB. Quite good for an ability that can't crit.
Your charge does 825 + 40%ultimate = 1155

Remember that this are the raw numbers. You have also 39 Magic Penetration plus 15% magic penetration to add.

Your opener btw is the Active from Deathfire Grasp:

UNIQUE Active: Deals magic damage to target champion equal to 30% of their current health (+3.5% per 100 Ability Power) with a minimum of 200 damage. 1 minute cooldown.

So we have 500 AP with this build which means you will open your assault with 47.5% !! -hp for the enemy. the rest is a two hit combo and he will be dead.

Now with this mastery build we will use the 2 summoner abilities: Exhaust and Ghost. Exhaust will be good to harass and shut down a champion while going through the defensive tree ghost will allow you to get in the frey without being scared.

Glyph: 1x Greater Glyph of Insight and 8x Greater Glyph of Focus(with just these 8 plus the items we will be perfectly at 40% cap)

For all those wanting to know why I have chosen this path, it is simple (It will blow your mind!):

1. CD reduction will benefit you by allowing your abilities to come off of cooldown alot faster than what it normally did.

2. With CD reduction that also means (defensively) that your W ability comes off of cooldown 4.8 seconds faster than what it normally did! So now for 5 seconds you have 25% movement speed, then will be able to use that ability again in another 2.2 seconds! (I know right, brilliant!)

3. Your offensive abilities are through the roof! Here is how:

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Devastating Blow

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Paragon of Demacia

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Heroic Charge

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Diplomatic Immunity

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Max Rank 4 12 8 100
CD Reduc 2.4 7.2 4.8 60

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Now I don't know about you guys but that amazingly improves Poppy's overall Offense and Defense. Her Heroic Charge will be up a lot faster now so that you have a greater chasing phase and her Devastating blow will be up 40% faster so that you will crush them. Her Diplomatic Immunity will be up 40 seconds faster than what it used to be which gives her greater and superior survivability compared to what it used to be. Not to mention that now when you have to run away from enemies you will have her 25% movement speed up "almost" 100% of the time.

Honestly, I can't stress enough how much this truly ups her gaming capabilities.

Poppy, in my opinion, is a great team player. For the most part use your ultimate Diplomatic Immunity to initiate for the team or to push with the team after the designated tank initiates. Also watch for any signs of pressure or focus on a teammate, as Poppy can graciously save the life of a teammate by just simply letting the enemy team know that you dont f*** with Poppy's friends as you ram their teammate against a wall. :)

*Poppy is great for teamwork so always make your decisions based on the good of the TEAM. Always be on your A game and make the right choices that will lead to a great outcome with Poppy. Its hard for some and it even gets me sometimes, but try not to be too greedy when it comes to playing Poppy. I know that your DB just hit for a ton, but sometimes a 1 for 1 isnt the best thing for the team, sure you killed the person, but you also died in the process, which still hurts the team and your lane partner (based on who they are playing).

Ok so as most people know poppy isnt the greatest solo. The reason I say solo in this section would be for a couple reasons such as:

1. You lane partner has died, and you are all alone.
2. Your team is fighting in mid against multiple enemies but you believe they are handling it well enough for you to just solo lane, but you know there is a stealth.
3. You are stuck with a 2v1 while your partner grabs a buff quickly or has to go back for items or health.

Now lets focus on these problems.
1 - If you lane partner has died it is best that you keep a fair distance between you and your enemies. Dont try and kill yourself because that will result in that lane being totally vulnerable. Instead keep a creep wave between you at all times. if they are pushing the tower together and your ult is up, position yourself; use it; then charge them into the wall. Now also be careful based on your health and situation. If you know you will be low after your ult is up and you still havent killed your marked target, DONT PUSH, unless you know for sure you could kill them in the tower range and get back to it. Wait till your lane partner is back and see the situation at hand before you decide whether or not it is wise to leave them all alone too.
2 - While Poppy is amazing for a counter gank or good to initiate team fights, sometimes you will find that when some of your team members are busy with a small team fight, it would be a waste to leave the lane as you know once you get there the fight will be over and you will have to go back to the lane you were in. Now there are some conditions to where when you are in a lane solo and there is a battle going on in a different lane, you stay there, but you know there might be a stealthed character nearby. The main is to stay close, maybe not in range but walkable distance, to your tower. Keeping a close distance to the tower will ensure your safety and you will still be able to kill creeps. If you get pounced on you will be able to DB them once and migh put the hurt on them to maybe wanna back up or you can pop paragon to get by the tower.
3 - In cases like this it is almost just like your partner dying, but they can get back to you quicker. The main thing to focus on is saving the tower from damage. Poppy can dive at people and do damage so keep the tower alive and keep yourself alive too. Most cases your partner will get the buff and even go around to set up a gank for you and could quite possibly be prosperous for you two.

*No match is perfect, sometimes you and your lane partner will get pushed back many times to your tower and you will just be going back and forth, but the main thing is to pressure them enough to not take down the tower while not taking damage yourself. Its tricky but sometimes you can pull it off. Play conservative when you must and play aggressive when you know, and only when YOU KNOW, that you can do something that will help out the team and not just you.*

-For the most part be sure to try and heroic charge always into terrain for the stun and bring the pain with the devastating blow.
-Try not to run into a death trap and dont mindlessly charge in with poppy and hope to accomplish anything.
-Your ult will save you in some cases, and will help you crush opponents, but remember, its 6 seconds. and by the time you put the ult on the enemy and charge them its almost up. Keep that in mind.
-Always remember the Paragon. When you are about to gank or you see that you're about to be ganked, pop the paragon for an extra edge on damage and some armor.