This is my favorite Poppy build. I really got tired of the build Trinity Force and then w/e. To me AP Poppy with spell vamp hits harder, plays better, and has great survivability. Great for interrupts and stuns, Poppy is great for creating openings in team fights as well as getting major kills.

Pros - Great burst damage
Very high Mobility
Decent CC

Cons - Low Health
Short Range
Not Great Farming

Marks - Magic Pen is a must. You're an AP Character.... so yeah.

Seals and Glyphs - Are kinda up for grabs. I personally like Mana Regen per level. They're a lot better later game when 15 AP from runes really isn't that big a boost. Plus, Mana Regen runes allow you farm with Poppy's Q ability a lot more effectively.

Finally Quints... Movement Speed is awesome. Just starting without boots, Poppy's movement speed will be 344 if you're using MS quints. This allows you to chase down opponents as well as run when necessary. Sure you can go Magic Pen or AP or Health, but I love that with boots 1, I have almost 400 movement speed. With boots 2 and W, 508 movement. Runes are all preference, but with MS Quints, no one is getting away.

Start with Heroic Charge. This allows you to catch up opponents and stun them. It's Great early starting game for waiting in the bushes stepped out and slamming them into a wall for the stun.
Max out Devastating Blow next. It's Poppy's main source of damage. At level 4 and 8 take points in Paragon for movement speed and max it out after Devastating Blow. Poppy's charge doesn't need to be Maxed until end game. One rank in it is plenty until 14.

On the flip side, you can max Charge right after Devastating Blow to do even more damage. And I've actually started doing this more often then not. Poppy is incredibly fast as is, so it's ok to sacrifice a lil speed for damage.

[*] Philo Stone - Good Regen for health and mana. This with Poppy's passive allows you to stay in lane for long periods of time. Plus Poppy isn't the best of farmers, so it helps keep the gold coming.

[*] Sheen - The best starting item for Poppy bar none. This basically doubles her damage from Q.

[*] Boots - Boots are all situational. I like Sorc. Boots personally. The Magic Pen is great for heavy hits. If the other team is heavy CC, then by all means get Merc. Treads. With whatever boots you get, just be aware of the other team.

[*] Lichbane - This item alone is crucial for Poppy. It offers more movement speed, AP, MR, and it uses 100% AP in addition to your next attack after the use of a spell. Basically Sheen on crack. I love this item because by the time end game rolls around, Poppy's Devastating Blow can be hitting around 1500 give or take a couple hundred. Also I prefer this item over trinity force. It's cheaper and allows for better damage scaling with AP items. Trinity Force scales with base damage whereas Lichbane scales with AP.

[*] Rabadon's Deathcap - I always debate between building this or Will of the Ancients, at least the order. Both are worth the added value. In RD's case, 155 AP plus an additional 30% of your ability power added onto it. If anyone is still standing after you get this item, I'm amazed. The ridiculous amount of AP this item gives is great. I know once I have this it's pretty much a done deal for any champion not a tank. Two shotting Teemo or Heimer is hilarious. Trust me you'll laugh. Anyways, I lean towards this item before a WoTA specifically because the added AP makes up for the Spell Vamp.

[*] Will of the Ancients - Great team item as well as good for you. It has a Unique Aura giving nearby Champions 30 AP and 20% spell vamp. Basically, this equals more SV for you and some for your allies.

That's pretty much it. If you're at the point you have those items, everyone should be dieing. Anything after those items is just gravy. To me it's also a bit better than most other AP builds. With most other builds, if Poppy starts takin damage she can go down quickly. Spell Vamp makes a huge difference in the survivability department. Deathfire Grasp is usually a core item for AP Poppy. I don't use it. Don't get me wrong. DFG with Poppy ult and combo usually is an instant squishy killer, but it leaves you without your ult and makes you too squishy in team fights for me.

Play Style

I Play pretty aggressively with Poppy. She's fast and hit really really hard. When Laning, take your time and play reserved. Yes I know I said I play aggressively, but keep in mind, Poppy doesn't have a lot of range and has considerably less starting health than a lot of champions. Use "Q" to farm and last hit when you can. The mana regen runes will help you farm easily with "Q". As for harassment, use devastating blow when you can, but mostly wait for a champion to get too close to a wall for a good stun. This allows your lane mate to get involved and you to follow up with a devastating blow. At level six, things get really fun. Poppy's ultimate allows for the best tower diving available. Six seconds of Invulnerability and increased Damage to the marked opponent. With a decent teammate, you can't tower dive and get away every time.


Team Play

Poppy is a great team player. Because of her high damage and low health, people like to focus poppy down quickly. The only problems with this is that Poppy's passive reduces all damage that exceeds 10% of her current health in half. Once more her ult makes her invulnerable to all other champions not marked by her ult. Basically, when a team fight starts or you want to start one, ult a champion that doesn't do any real damage and start hammering down the opposing team's dps, casters, or other squishies. It makes team fights so easy when all the dps is running from you and not focusing on the rest of your team. Also, Poppy's charge allows you to single out opponents for your team. Pick out a champ you wanna kill. Charge them back to your team or slam them into a wall for a stun. This also works in reverse. Say your ranged carry is running for their life. Charge the chasing opponent to open up some space for your teammate to escape then use your speed to get away.

Summary, Poppy is a fun champion to play. She hits incredibly hard and is great at initiating and controlling team fights. The spell vamp keeps her alive and in the fight and allows laning longer without backing. Have fun playing her. Please leave me any questions or comments you might have. I'll try to answer them all.