AD

Here is the build I use on Poppy. When our team composition is good, I usually end up 20+/5-.

Utility :
-Assassin
-Pusher (end game)

Pros and Cons :
-You need a team to cover yourself once you have done your abilities and running back
-You can initiate a team fight
-You will one shot squishies
-You will move fast

Tips :
-Hide in a bush close to an exploding team fight. Locate your target (the msot squishie usually) and then use ult on it if you wanna burst it under 1 sec and flash away or use it on the lowest damage/cc champion. If they are way to busy to notice you, keep your ult for defensives purposes.
-Don't play her vs teemo/singed her passive get ignored.
-Between level 3 and 6 when you lane, go gank mid when he needs help, shes an awesome ganker.
-Oracles wards and potions are your best friends.

AP

Here is the build I use on Poppy. When our team composition is good, I usually end up 13+/2-.

Utility :
-Assassin
-Tank Destroyer

Pros and Cons :
-You have shorter cooldowns with DFG/runes, so you can use your abilities more often and dont really need to back much after an attack.
-You can initiate a team fight
-You will one shot anybody
-You will kill fast

Tips :
-Hide in a bush close to an exploding team fight. Locate your target (the msot squishie usually) and then use ult on it if you wanna burst it under 1 sec and flash away or use it on the lowest damage/cc champion. If they are way to busy to notice you, keep your ult for defensives purposes.
-Don't play her vs teemo/singed her passive get ignored.
-Between level 3 and 6 when you lane, go gank mid when he needs help, shes an awesome ganker.
-Oracles wards and potions are your best friends.

AD

Armor Pen runes are a must because your build takes a while before reaching an item that gives some.
Mana regen runes will help farm and prevent getting too much starved early game.
Cd reduction runes are really good to reduce the cd of your charge which usually makes you initiate your target. It, of course, reduce the devastating blow cd, but its better for her charge/ult.
Movement speed runes are really good to escape/chase.

AP

Magic Pen runes are very good to farm and harass, it's better to use glyph runes into cd reduction since void staff is gonna get the pen for you after.
AP runes will help farm and do some more damage early game.
Cd reduction runes are really good for your Q, that more u use it the more

Nothing very special here, Greed is good to help her get some gold with Philo stone. Let your mate farm minions.

AD

Regrowth / Philo
Really good item to farm, and makes the fact of getting harassed forgiven.

Boots
Mercury are a must since you are just showing yourself for a few seconds before disppearing again in a team fight.

Sheen / Trinity
Yes, core item

Phantom Dancer
Some people would get infinity edge here instead. I prefer Phantom dancer for the simple fact that you run way faster.

Infinity Edge
No comment needed

Last Whisper
The armor pen you needed. This is for tanks because by this time they will have a decent amount of armor.

Bloodthister
Prevents your help going down slowly. Easy damage.

AP

Regrowth / Philo
Farm, mana regen, harass protection

Boots Mercury
Protects from Dot and ake you always able to attack when needed

Sheen / Lich
Core item

Kage / Deathfire
Easy farm for gold to get giant belt which give you a decent amount of health

Rylai
This item is really good. Gives you health and makes your target that survived to your Q and E unable to escape.

Void Staff
Core Item, item mainly for their tanks

Rabadon
They will have surrendered before you get that item. If not then have fun one shotting w/e you click.

Flash + Charge = Ouch for them, also a good way to escape.
Ignite is just to get kills that you cant reach anymore after using Q and Charge.