You Prioritize Q, then E, then W.
Q plants have the longest attack range, and Q itself can set up plants behind minions without drawing their aggro, killing them, and shunting your gold gain from trinket. If Q plants don't immediately attack a champion, you may have to auto attack them, but that's generally okay, because Zyra's attack range is generally long for a mage.
If you time Q use correctly with 2 spread out seeds, you can deny opposing adcs their cannon minions, because they'll be more worried about the damage they are taking.
E is secondary, because increasing the root is important, and the on board damage of the skill is more reliable and this more important than getting more seeds from W. If you wait too long to build it up, you'll find opponenet defense sometimes creeps up on you and makes you less effective.
Fully utilizing E:
-Generally you want to cast it either after you have already Q'd into 2 W's OR you want to cast E first, and then cast 2 W's and use Q to activate them. You rarely EVER want to proc W with E, because the attack range is low, and thus the slow isn't that effective.
- Wait to use it until you an guarantee it will hit. In other words, if Master Yi is running at you ulted, do NOT cast E, or you will guarantee your death. Cast Q > W W, wait for him to alpha strike to try to dodge the damage/ get to you, R yourself, and then when he lands from Alpha strike, E him. This will root him long enough for the R to activate, and follow with a knockup. Hopefully if you did this exchange right, you got away, and at least heavily damaged Yi, while he didn't kill you, and maybe killed him.
Zyra's kit isn't hard at all. What is hard is learning timing, and to be patient, rather than button mashing. She has low cooldowns so a new player will always be apt to button mash.