There aren't many rune choices on poppy, 90% of the time you will just take phase rush. However in some games where the enemies are running a very ranged heavy composition (4-5 ranged champs) then predator can be a better choice than Phase rush. Predator will enable you to have stronger early ganks and also in teamfights allow you to get ontop of the enemy without having to use important cooldowns such as flash or your e.

As for the secondary tree there are two main choices; firstly is precision and taking triump and Legend:Tenacity, you take this setup when they enemies have a lot of cc that can be reduced by tenacity.

The other option is Inspiration and taking Cosmic insight and hextech flashtraption; Cosmic insight allows you to have flash more frequently which is a really useful tool to reposition to land your e stun. Hexflash is a funny rune but once you get used to it you can find some really creative ganks bby dodging vision with hexflash or by hexflashing the walls on bot or top to dive.

Poppy is strong in jungle skirmishes and dives, aim to fight in locations where you can land your e. Usually this will be in jungle fights and in bot/top dives, fighting around mid is hard usually due to there not being many walls to land your e on. Poppy is an extremely strong diving champion as you can land e reliably into a wall or the tower and burst a champion in your cc, and if the dive doesn't look so good after that then you have phase rush to escape the tower. Poppy falls off slightly late game in terms of damage and tankiness but becomes more utility based with her e, w and r.

Poppy is a fairly simple champion so there aren't really any indepth combos. The only one which you may not know about is q into tap r, this allows you to land both instances of your q damage onto an enemy champion as in the 2nd q they will be knocked up by your tap r. This is a useful combo when you either don't have or can't land your e stun as it enables you to get your full damage out.