Poppy's early game is one of the strongest early games in the game. Although poppy is a tank, landing a full combo onto a wall is extremely devestating in the early game, as u can 1 shot about anyone who is around half hp (and even more, especially with electrocute). Hitting your E properly into a wall is the core of poppy's kit, and thats where a good chunk of her early game power lies. However, it wont always be possible to hit ur E into a wall, so in these cases u should either reposition or if ur stronger than ur foe anyway, u can still fight him.
Ur Q is another essential part of ur kit, and while it is pretty easy to land against a stunned target, making the Q's second part hit can be pretty challenging. in order to do it, u should aim ur Q a bit to the side where u think ur opponent will go.
ur W has 2 main uses: first, its for the movement speed, which is pretty straight forward. The second use for ur W, however, is to cancell the opponenet's dashes. itt can be either used right when ur opponenet dashes, or u can use it before he dashes to ensure he wont dash for the next 3 seconds. landing ur W and cancelling ur opponenet's dashes is extremely important and its one of the things that allows u tocounter many mobile champs (note that it only works on dashes, so it wont work on blinks such as "Flash" and Katarina's E).
Poppy's ult has, once again, 2 uses: if u tap it, it will be an AOE abillity that knocks up foes with a relatively small radius. It can be used to extend ur basic combo (E-AA-Q-AA-R-AA). The ult's second use is to hold it. Holding ur ult will make it launch a long range attack (similar to Braum's ult in appearence) that will launch enemie champions in the direction of their base. i like to do it in order to isolate someone in a 2v1 by launching the other one far back.

in temfights, poppy should supress one target (prefferably the enemie's carry) so that her teammates can kill the target.