this build maximizes poppy's magic damage, attack damage, and her 2 hit K.O. legacy. With this build you would not need to buy boots,items for attack speed, spell vamp, and lifesteal seperately because it is already provided by trinity force lich bane and hextech gunblade. the hextech gun blade also will allow you to increase your a.p and a.d at the same time in a high amount. bonus mana, health, ability power, and attack damage is also given by both trinity force and lich bane to make poppy a semi tank.

SEAL- DODGE(for semi tank properties)
MARK- ARMOR PENETRATION(for 150% bonus dmg from trinity and 100%ap to ad from lich bane)
GLYPH- COOLDOWN REDUCTION (so you can use your hammer and charge skill more often)
QUINTS- COOLDOWN REDUCTION or ARMOR PENETRATION (depends wether you like more damage or using skills more often)

PROS
+2 hit k.o
+inc. both ap and ad at high amounts
+awesome first bloodkiller
+semi tank(as long as you keep hitting an opponent<LIFESTEAL(50%) & SPELLVAMP(50%)>)

CONS
-expensive build but possible
-needs a partner in early game
-easily harassed by long range opponents

Buy DORAN's SHIELD FIRST<IMPORTANT> so you would not suck in early game.

then complete SHEEN (amplifying tome first)

then ZEAL(gloves first)

then PHAGE(RED CRYSTAL FIRST)

complete TRINITY

then BILGEWATER CUTCLASS(vampiric scepter first)

then complete HEXTECH GUNBLADE

then go for LICH BANE

then buy a HEXTECH GUNBLADE or PHANTOM DANCER

then buy INFINITY EDGE


lastly buy a RABADON's CAP

always last hit creeps you will need lots of gold. If you see a lot of creeps on other lanes and no one's around teleport there or simply run.
Make a visit in the jungle often if possible kill your enemys' jungle creeps too xD

awesome partners for poppy are SION(stunner), CHO GATH(HARRASS), BLITZCRANK(FISHER).
these champs will help poppy in her early game to fatten up.

when poppy is harassed in early game ask for a switch lane or a partner change see which one best suits you