At the start of the game you need to be sure to go at your lane as fast as possible. This is because your seeds will then all / almost all been spawned at the lane itself. When you engage you need to be sure to land your "E" first, then you land your "W" twice with a "Q" afterwards. When you have your ult up you have to use this combo: First "E" , then "W" , then "R" and as last your "Q". The last two orders of the combo is free to use in which order you want. You can use "Q" first before "R" too.

HINT:
Take barrier instead of Teleport if you are playing against a hard counter.
With this build you can burst an enemies health a lot in one combo. But be careful, Zyra is more an early-mid game champion than a late game champion. So try to roam and get kills in the early-mid game.