Poppy actually makes a pretty decent support with and against many ADCs (but not all), and I have also had success in mid lane and as unconventional bot lane carry with healer support; but I will limit this post to top and jungle.
I would argue that you should NOT get very aggressive masteries in top lane; Poppy's late game takes care of itself and you need to concern yourself with getting through the early game. In the jungle, however, you need to make your clear time as fast as possible. I like 13/17/0 or sometimes even 0/27/3 for top lane, but 22/5/3 in jungle. I'd recommend that you only go 21/9/0 or other aggressive masteries if you know who your opponent is and you feel confident you will beat them and want to do so as hard as possible.
(Top lane) Flat AD reds are OK but hybrid pen is probably better. Poppy has strong autoattacks but also has a lot of magic damage on her Q (and her E, but you do that more for stuns or movement than for damage).
Movement speed is very important for Poppy, so MS quints are a fine choice, but armor or health regen quints are very valid choices to strengthen her early game.
I usually start Crystalline Flask and 3 red pots, but Doran's Shield and perhaps Blade work as well.
Max Q first in almost any situation unless you really want to max W for extra armor.
In top lane, you want Sheen ASAP for the huge damage boost on your Q (and bigger mana pool). If you would rather get Vamp Scepter for sustain, that's a valid choice, especially if you find yourself trading a lot of autoattacks. No other damage items are comparable to what you get from Sheen. Only get other stuff if you are getting wrecked and want to focus on defense. Rush Trinity if at all possible, Sheen then Phage then Zeal.
(Jungle) Attack speed runes are key since her autoattacks are naturally strong with her W already. I always start W but Q is likely a little faster if you don't mind being low mana by the time you get blue buff and probably a bit lower health. Rush the AD jungle item, or Trinity if you're very gank-focused, or Wriggles if you're really concentrating on jungle farm. Max Q first.
I usually go Hextech Gunblade in top lane and BotRK in jungle, but really it's up to you which one you get in either situation. Getting one of them is strongly recommended IMO.
Aside from Trinity and whichever Bilgewater upgrade, you can get more attack power or focus more on tankiness; those two items make you really strong by themselves. (The Trinity buff adding to every Q you land is pretty huge: you'll notice your power level really jumps when you complete Trinity.)
Defensive options include Randuin for armor/HP tank; Spirit Visage for MR/HP tank and CDR; Frozen Heart for armor, mana, and CDR.
You'll notice quickly that Poppy is SUPER mana hungry. You can either be very careful with your mana expenditures and/or recall often, or you can consider buying Chalice of Harmony or possibly Tear of the Goddess.
Maw of Malmortius is a good buy sometimes to balance MR and more damage output. QSS into Mercurial Scimitar is an item I really like if the enemy team has suppressions because they usually seem to like targeting Poppy with them. (Skarner, Warwick, Malzahar) If you get lucky with your ult, though, sometimes they will waste their ult while you are invulnerable to their suppression! QSS can also help against other extremely strong CC like Nasus's slow.
IMO Poppy's greatest weakness (aside from magic DOT cutting bypassing her passive and high natural armor) is CC, so I usually get Mercury Treads unless the enemy team's CC is weak overall or isn't mitigated by Tenacity. In that case, Swiftness (+3 speed, slow mitigation) or the CDR boots are probably better choices. Mobility (+5) is also an option.