Poppy is a Hybrid champion that is because of her passive virtually impossible to solo kill. Ignite is the best counter to her passive. If you can get her low enough and ignite you can kill her; however played right you wont do this before dying to her yourself.

Note: Watch out for Kha'zix as he counters Poppy Top very bad.

Poppy can solo 2 players top and even up to 3 if played correctly.

Note: The lower poppy's health the harder she is to kill. People love to tower dive when poppy is low. This is the perfect time to punish them for this. Use walls and terrain to stun them near or under your tower and Q to finish them off.

The difference between a good poppy and a bad poppy is landing charge correctly.

Flash and W are a good tool to get behind the target and push them in the oppisite direction

Baiting into 5 players to have them chase you into your team then reengage even if you are low can be the difference between a win and a loss.

Keep in mind Poppy is a great champion for getting past the tanky walls and therefore good at taking out ADC and APCs.

Personally I have chased 5 people across in and out of the map killing them one by one as it is very hard to escape poppy.

If you are the target every fight, good job. You just won, since killing poppy through her passive takes so long that they are being wiped in the mean time by your team.

Another less tanky version option is also available this would be

1 4 4 0
0 3 0 0
1 1 0 0
1 3 0 0
1 3 x 0
x 1

in the dps tree. Note that this version is less tanky and may need a little more defensive runes or items depending on who you are facing top.

Poppy is a very aggressive champion with high burst, survivability, and CC.

Do not be afraid, however, to become a tank for your team. Building tankier doesn't mean you will contribute less to the team. Poppy still does high damage and sometimes being the forced focus of the enemy team can change the tide of battle to ensure kills for your ADC.

Sometimes I even use poppy to support. CCing the team guaranteeing kills for my team mates if not myself included.

NOTE: If you find you cannot keep up with the enemy team or in draft you see a lot of high speed champions. Fleet Foot in the support tree first row is also a great choice.