The early game of Zyra should be agressive, as we have said before, poking with Electrocute is really easy and deals a lot of damage.

You should poke by using Q + W + W + aa
Zyra has a good amount of Mana Regen, so you can poke a lot without going base.
Your combo should be E + W + W + Q in Early game, you root somebody, and make that entire combo.

When you reach lvl 6, just play the combo that has been mentioned before, E + W + Q + W + R.

As we are playing with Electrocute,your poking is simple, just Q + W + aa will aply Electrocute and deal almost 2/5 of your enemy's life (If he isn't a tanky one)

Then, your best combo is easy, E + W + Q + W + R for having 1 plant of each type.
Later on, you have some ways for playing this combo.

- If your Q is used close to your seeds (W or Passive) the seeds will transform into ranged plants, that hit enemies (DPS)

- If your E is used close to your seeds (W or Passive) the seeds will transform into melee plants, that slow enemies on hit (CC)

So you'll have to play your combo thinking about what your plants can do, that will carry almost every fight until Lane Phase ends.

Then, Zyra has an agressive playstyle on Teamfights, try to hit R with slowing plants to at least 2 people inside. Your team will deal the most important part of the damage, your job is trying to keep enemies inside the teamfight with your R the most time as possible, as your R will deal almost 700 DMG + your plants + Electrocute, you will win the teamfight almost always.

There are such a lot of ways to play Zyra. Here I recommend you other ones:
You can start your Burst Combo with E + Q + W + W + R
This will make your seeds to go on Ranged plants, this type of combo is used for DPS.
You can play Zyra on Roam, if you want to, just max Q and roam mid as much as you can. For doing it, try to do a good engage without R at botlane, helping your ADC to get the kill, and then go to mid with your full combo for giving some kills to your mid laner.