It depends on what your problems are. Laning or grouping? Trades and csing or peeling and teamfighting?
In lane you just play safely until you get your first item. Depending on your opponent and your play style, you want to rush one of the following items:
,
,
, or
. After that you should be able to 1v1 your opponent in extended fights with your q, passive and grasp.
When it comes to wave management, I prefer to get a sun fire whenever I can so that I don't get pushed into tower so easily (your early wave clear is pretty bad). After two components you shouldn't be able to die to trades if you properly manage your shield.
Once you start grouping, you should be peeling for your back line above engaging; if you win a fight, you are good at re-engaging but in the end you shouldn't go for picks unless you know your team can follow up.
Some final things on poppy:
1.Your q is your trading tool. Landing it is imperative to winning trades.
2.You can charge grasp with sunfire in a minion wave to get some bonus harass on your opponent from shield as well as a heal.
3. If you land an e q p combo, you almost always want to go for the shield before they can retaliate to negate the majority of their trade.
4. Your ult does about 150 damage to opponents when you first rank it, so make sure you keep track of how much health they have under tower. You can combo them onto their tower and ult to finish them.
5. Sometimes, an instant ult is just as effective if not more effective than a charged one. Don't bother trying to always use it when it's charged.
6. If you lose lane, just keep building tank and be a big disruptor to the enemy engage.
If there were one thing I think you might have a problem with is being too aggressive. All the champions you listed tend to like being near the front soaking damage and disrupting the backline. Poppy wants to stay near her backline more often than her enemies, so be an anti-aggressor and peel as hard as you can.