Hello Guys!
That is introduction to my guide about Zyra.
I see Zyra, as burst-run-burst champion.
Lets talk about it more.

I Prefer:
Marks: Greater Mark of Insigh x9 for 29 magic penetration with Sorcerer's shoes
Seals: Greater Seal of Replenishment x9 for comfortable laning, with masteries and doran ring we have enough mp5.
Glyphs: Greater Glyph of Knowledge x9, more ap -> more burst dmg)
Quintessences: Greater Quintessence of Potency x3 - it is my choose, i prefere more AP

Nothink extraordinary. 22/0/8 or 21/0/9. If you love 9/0/21 - you can use it too.

Start with Doran and keep laning. You have enough mp5 for harrasement and e skill for keep distance.
I Prefer build my Zyra with some items with HP, such as Rylai and Roa. Thats enough for start teamfight, deal your burst damage and use zhonya/keep running away. After few seconds you can return to battle and deal more dmg by your skill:)
Lets talk about shoes.
I Prefer Sorcerer's Shoes with magic penetration - it helps to deal more burst dmg, and so on.
Also, with 9x Greater Mark of Insigh you have 29 magic penetration, it is enough for kill some ad/ap carry with low 30 magic resist with your burst.
I DONT LIKE CDR BOOTS. I think it for supports ]:->

Get e skill first, it help to do good pull and keep distance from enemy's jungler/laner.
So, 2nd level give w skill to you. It is a good combo, W, W, E
you grow 2 plants and keep enemy near for 1 seconds, its enough to good harrasement.
3,4,5 lvl i get Q skill. good cd, good damage. I Prefer combo Q-W-W-E-Q.
It so painful to your enemies :)
And so, at 6 lvl you get your own Ultimate.
That skill is good addition to your combo. Now it Q-W-W-E-Q-R-Q with some cd befor last Q.
If yoy have zhonya and enemies focus you - push zhonya after 2nd Q, and after it do Q-E-R-Q