My name is Atamillia, I'm Platinum 5 on NA server at the moment.
I play fairly casually, but Zyra is my favorite champion so I decided I would share the way
I like to play her in hopes that someone can read this and finds success in playing one of the
funnest supports in League.

A lot of Zyra players will max E first, personally I think Q is the superior choice.

Q increases damage and lowers cooldown as you level it, where as E gains damage and duration.

You should always be harassing your enemy, and if you're using your E to harass then you have nothing to protect yourself if you're ganked or the enemy decided to run towards you.

Always W before your Q or E, they have a delay and it will instantly spawn the plant when the spell hits.

To harass in lane:
W>Q (try to toss an auto or 2 in there as well)

To engage:
W>E>W>Q (try to lay the first W behind them so that they are slowed longer if they run, and second W in front so if they choose to fight they have to tank the Q plant)
Use your R at the end of this combo if you're trying to kill.

To disengage:
R>W>E>W>Q
This will waste the attack speed buff your plants get, but your enemies will almost always take the shortest way out of your ult, leading for an easy E and guaranteed knockup.
This combo is a little risky though because they could flash your ult, making it useless.

W>E>R>W>Q would be your disengage combo if you didn't want to risk your ult missing.
Try both and see which works best for you.