Hello Mobafire. This is a -tentative- guide to Zyra, The Rise of the Thorns.
Zyra is an AP and location based mage whose spells invoke the plants around for damage, and can even grow large plants that attack on their own.
The key to using this guide to play her is maximizing your versatility in combinations, which will be touched on later. Without further ado, I hope you find the rest of this guide useful.

Pros
+Strong sustain and burst
+Variety of CC
+Excellent harass and farm
+Tons of AoE
+Versatility

Cons
- Low Mobility
- Skillshot dependent
- Very Weak against strong chase/closers or high mobility
- AP dependent

These are the abilities I take by level.
Abilities:
Rise of the Thorns When she dies, Zyra transforms into a large plant over 2 seconds, and can activate any of her abilities to fire a Vengeful Thorn. This is a single skillshot nuke that deals a large amount (99+25xlevel) of true damage to everything it hits in the line.
It's very powerful, so it can be used to secure someone escaping from you with almost no health left. Don't rely on it to secure kills though...

Deadly Bloom Zyra causes a bloom to grow at target location. After a brief delay it sprouts, dealing damage in a small radius around it. If a seed from rampant growth is within the radius, the seed sprouts into a Thorn Spitter, a large plant that fires on enemies from range. Lasts for 10 seconds, and can be attacked and destroyed.
I take one rank in this early for the damaging poke, and max it second, as it's her most powerful damage dealing ability aside from her ult.

Rampant Growth Zyra grows a large seed at target location, revealing the area around that location for 30 seconds. Any enemy champion that steps on the seed is revealed for a short duration, and the seed is destroyed. Any seed in the area of either Deadly Bloom or Grasping Roots grows into a powerful plant ally that attacks nearby enemies for magic damage. Rampant growth also passively increases Zyra's Cooldown Reduction with each rank, up to 20% when maxed. Zyra can store and carry up to two seeds at once, and have 4 more planted on the ground. Planting a seed costs no mana.
I take this at second level and max it by 9th. While it might seem counter-intuitive to take this over the raw damage of Deadly Bloom, I prefer the very strong harass that the plants can provide, as well as the very rapid reduction too my other cooldowns.

Grasping Roots Zyra sends out a line of roots to damage and snare enemies caught in the spell. A seed that is struck by the spell grows into a Vine Lasher, a large plant with short range attacks that slow the target for a short duration.
As Zyra's best CC, I take a point in this at 4th level, but max it last. The damage it deals isn't as high as Deadly Bloom, and the CC is fine without needing to be increased to higher levels.

Stranglethorns Zyra's Ultimate, she grows a thicket of vines in a large radius that damages enemies in the radius. After a short delay the vines snap up, knocking enemies into the air. Any Vine Lashers or Thorn Spitters that are struck by the thicket of vines are enraged, attacking 50% faster.
As your ult, you should take ranks in this whenever possible.

Starting choice:
Doran's Ring Nearly everyone shows up at mid with boots and health pots. I personally don't need the health pots, and though the mobility is nice, I like the bonus AP and mana regen slightly more.

Boots: Sorcerer's Shoes These are the only ones you need. The Ionian Boots have a nice CDR bonus, but because you'll hit the 40% limit anyway, the spell pen benefits you far more. None of the other boots will really help you, so they have no place here.

KEY ITEMS: Athene's Unholy Grail and Rabadon's Deathcap
First: The Unholy Grail is a beast of an item on Zyra. The bonus AP is wonderful, the Magic Resist is a nice touch for mid lane, and the Cooldown Reduction and Mana regen mean that you can use your spells just to summon plants to harass your opposition without fear of ever running low on mana or spells. And of course, endless farming.
Second: You're a mage. The deathcap has a big floppy brim, and lots of AP. 'Nuff said.

Other items:
Will of the Ancients Spellvamp and AP. Because the plants you summon are abilities that deal magic damage, they'll heal you with every strike while you have spell vamp.
Void Staff AP and magic pen. You're a mage. If you finish a build and don't have this, you should be beat over the head with it by an AD Carry.
Rylai's Crystal Scepter Health, AP, and a nice slow to your spells. By now you need the bonus health, and the slow effect, like spell vamp, is gifted to your plants as well.

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Alternatives:
Zhonya's Hourglass Great AP, nice armour, and one of the best activated abilities for Zyra. 2 seconds during which they can't kill you, but your plants can kill them? Great!
I don't use it as a main buy because I dislike the idea of being rooted in place for 2 seconds, and this can remove other items that are more useful for offense from the build.

Abyssal Mask AP, Magic Resist, and an aura that reduces magic resist.
Great if you're having trouble with an AP nuke or if their team is really stacking the magic resist. Otherwise... not so much.

Deathfire Grasp AP, Cooldown Reduction, and a lovely activated ability. If you're really after a specific target this is a great choice... Otherwise there are other choices out there.

Main Runes:
9x Greater Mark of Magic Penetration
9x Greater Seal of Replenishment
8x Greater Glyph of Scaling Ability Power
1x Greater Glyph of Scaling Cooldown Reduction
3x Greater Quintessence of Ability Power

Why?
These runes maximize your early game, while giving you some lasting power into late game.
The Glyph of Celerity, combined with masteries, Athene's Unholy Grail and your Rampant Growth means you'll have completely maximized your Cooldown Reduction with next to no cost to yourself.

This guide is far from finished, but I realize I need to go before I can finish it.
I still need to:
List alternative runes
list masteries and explain them
list viable summoning spells
Explain in depth strategy for laning and team fights
Improve the visuals in this guide.