So after playing 6 games with Precision and 6 games with Domination I've come to the conclusion with my play style and not really changing how I play or approach situations I prefer Precision as my secondary runes. Domination does more damage statstically but I notice not being able to finish the kill that I don't really see happening with coup de grace. Then the ability haste you get from ultimate hunter really isnt that noticable because the cooldown time seems pretty fast once you get malignance and having the Presence of mind mana regeneration seems to pay out more. So with that being said that is why I'm recommending the Sorcery/precision Rune page set for Zyra.

Start: Place ward jungle, hide in first jungle camps bush until 55seconds, walk out and place your seeds until mob spawns, Q auto and walk to lane.

Keep distance but don't let them bully you. At level 2 you can start placing your seeds(W) with your Q for good pokes. work towards getting regular boots and your whole first item. You want liandry's Torment first before Sorcerers boots.

I try to only use my Q with 2 Ws and that's a good way of juggling your mana flow. If you have 2 seeds use an ability.

You can try to practice only pressing your W if you think you're going to hit them with an ability because it kind of has a delay in a sense. your seed doesnt need to be down before the abality. Another thing try to place it off to the side of the person your attacking and never on top of them, that way they don't kill your plants right away or anything.

Zyra is really good at escaping but time your E's right to root them and always to get a E plant out so it slows your enemy. Don't be afraid to use your Ultimate either if you need to escape or save someone even though you don't have plants out.

A fun thing I like to do is walk over to the dragon before it spawns and gather a bunch of seeds down then when it spawns Q+R and make a crazy frenzy that melts the dragons. Only do it if you know it's safe and your adc is backing and you dont wanna push the wave or something like that but it's still really fun.

Mid/late game:
Remember to play for the teamfights but just hit an ability and keep running back don't R unless someone on your team is about to get got. It could save them and get you an easy kill. Zyra's auto attacks are not strong and I dont suggest relying on them often in the mid/late game. Let you're plants do the damage for you.

If your carrying and have loads of gold at full build. Switch your support item for storm surge. You can also drop boots for shadowflame. You can also just not use Rylai's and use Stormsurge instead if you're doing great early game.

All in all Zyra is my favorite champion as a beginner to League of legends. Recommend for all people new to the game.