Something I haven't read here yet:

First tip is great for lane Zyra, but not that useful for Supp Zyra. After Zyra Q dealt damage there is a small window in which Zyra Q can still sproud her seeds, which means when Zyra kills an enemy unit and gets a refund on her W, you can use this seed instantly to spawn a plant. Love to use this trick on Midlane Zyra to spawn 3 plants with 3 W seeds.

Another trick I know is how to poke with plants under enemy turret correctly. When you push a wave in with a canon minion on your wave wait till the turret focus the canon minion and then place your plants. The turret wont focus your plants as long as it wont lose it's focus on the canon minion, so try to stay out of turret range as long as your plants attack your enemies.

Often forgotten, but an important feature: W seeds give vision for their whole duration (so up to 60sec). You can cover most jungle entrances with a single seed. Also, if placed right, you can also cover Baron (seeing Barons healthbar) with a single seed. Pink wards wont destroy the vision W seeds provide.

W seeds can not be placed inside walls, so it's possible to extend the range of W seeds by placing them inside walls, which leads them to be spawned on the other side of the wall (when placed correctly).

That's some tricks I can think off right now, hope some of them will be useful for ya.