(This is a work in progress. Please suggest changes and point out mistakes. Thank you!)
Poppy is usually played as a hard tank, but once I saw the potential of her passive combined with the Rapid Firecannon, gears started to turn. I used to call this build "Dunkmaster Poppy" as most of the damage came from her Q combined with her E. I have a modified version of this build with the same name which is also viable, but not as much fun in my opinion. Running people down with Steadfast Presence and chucking your buckler of death at them seems a lot more satisfying.

The Point of this Build

This isn't meant to be the most efficient or the strongest build, but it's meant to be a build that focuses on the fun of Poppy's buckler chunking everyone's health down and smashing them into the wall to finish the job. It turns Poppy into a ranged/melee assassin/tank.

Items

The heart of the build. Gives her the speed, armor, health, and the massive auto's she needs for her Passive.

Helps with all of Poppy's stats, gives Spellblade for massives attacks, and gives her the crit she needs to reach 100% at final build.

More speed for Poppy. Furor will help chase down your prey when you have the Firecannon, as you can catch up extremely quickly after one auto.If the carry is AP or they have a lot of stunning abilities, then choose Mercury Treads or Ninja Tabi if their ADC is problematic. Boots of Lucidity is useless because of the CDR from the Essence Reaver, and magic pen or armor pen isn't worth it.

Turns you into Captain America. The range increase, movement speed, crit, and attack speed will stack on top of the rest of your items to turn you into the faster Tank/Assassin on the rift.

When combined with the mastery: Intelligence, tons of crit, and damage, this lets you spam your combo's and chase faster with your W.

Makes your Buckler chunk your target's health into oblivion. The bonus damage from your buckler, Firecannon, Dead Man's Plate, 100% Crit, Spellblade, and Furur's movement speed bonus will annihilate their health and make them cry as you bolt towards them with 600+ movement speed and your E on cooldown.

Reasoning Behind Each Item

The heart of the build is the Deadman's Plate. This gives Poppy an extra boost in the armor, health, and speed department. It's what makes her able to run down her opponents when combined with her W.
Trinity Force is amazing on Poppy, giving her pretty much extra everything. The crit she needs, movement speed, attack speed, CDR, health, mana, and one of the deadliest parts of her. The Spellblade. After you smash someone into a wall with her E, it activates the Spellblade and makes the next auto attack hurt like hell. Combined with the Deadman's plate, the auto hurts even more. Q'ing the enemy while they are still frozen will reset the Spellblade and let you have another free hit. If they flash out, by the time they're too far away you'll already have your buckler back and with the range of the Firecannon, you can snipe them. If they still persist, you can run them down with Steadfast Presence and do it all over again.
The combination of Statikk Shiv and Rapid Firecannon seems a little excessive, because it is. The overkill of that one auto attack, that one buckler, that one shot. It's what makes this build so fun to play. When combined, the energized attack will trigger Deadman's and combined with the bonus magic damage of her passive, smash the enemy's health down. Then you can dash into them, auto them, E, auto again with another powerful blow, Q, auto, and if they aren't dead yet from the first auto, you can double tap your ult to knock them up and use the Spellblade auto again. Combined with the energized attack, Deadman's, Crit, and Spellblade, you're pretty much guaranteed a kill from anyone unless they build heavy tank, CC you, or stun. If you can stay alive for a few second, you can get the kill.

Runes

Pick your favorite AD/Tank runes and watch the magic happen. It's that simple.

Masteries

Everything in the masteries increase Poppy's damage and keep increasing if you do more damage. Double Edged Sword will increase damage but since Poppy is so tanky, it's a great tradeoff. Assassin, Oppressor, and Merciless make it to where if you are alone, chunk their health, and smash them against the wall, you're golden. The extra CDR from Intelligence lets you combo more frequently, the Spellvamp and Lifesteal reward you for the combo, and Dangerous Game lets you 1v2 and 1v3 better. Speaking of which, if you ult their tank and kill their ADC in a teamfight, you can pretty much just snowball while you watch them run away from your buckler hurdling towards them. To wrap things up, Wanderer makes you an even more mobile Tank/Assassin if your TP is down, and Thunderlord's because... Thunderlord's.

Laning...?

I won't explain laning because there are plenty of guides that can explain it in more depth than me. For the sake of this build, I recommend abusing your passive any time you can if you have Firecannon up, and playing it safe or hiding in bush until they're near a wall. If you are against a ranged champion, waiting in bush until you can smash the enemy laner into your turret range or taking the Rift Herald when Toplane is empty is a good way to get ahead without risking it for CS.

Team fights

The most troll-y and most annoying way to win a team fight as Poppy is to ult the enemy team's carry or tank out of lane and bully the support or midlaner. By the time they get back into lane, the support or carry is probably too low health to re-engage, so if your jungler is nearby you can Leeroy Jenkins the rest of their team into a pincer tactic.

Buff Steals

1. Ward Dragon or Baron.
2. Wait for enemy team to engage and clump together.
3. At 800-1500 health (depending on champion level) charge ult and send the jungler/most of their team blasting off.
4. Flash in and burst the buff.
5. Profit.

Conclusion

Just have fun with this build. It isn't meta, but so is Poppy. I love this champion and I've spent hours testing dozens of different builds for her, this being the most enjoyable to play. Remember that this won't always yield great results as the situations in league are nearly infinite. Just because it works well for me doesn't mean it will for you, but if you follow my guidelines and practice the champion, you should have similar results.
Thank you for reading! Please post any suggestions in the comment section.