Zyra Mid is insanely strong right now, mostly due to new runes and the fact that she can provide consistent DPS in a meta that's not exactly burst friendly. That's not to say she can't burst, though.
The biggest mistake I see people make is making sorcery their primary tree. In reality, it should be Domination primary/Sorcery secondary. Electrocute on Zyra does and absolutely insane amount of damage. One of Zyra's best combos is E>Q>W>W, placing 2 seeds down before Q can pop. Obviously this would proc electrocute. What people DON'T know is that in lane, Q>W>W will pop Electrocute almost instantly. This is because technically the two plants are separate, unique spellcasts. That's....a lot of damage. In fact, once I get my Morellos, I can half HP my lane opponent with a single QWW combo.
The second domination rune I take is cheap shot. At first, it's only OK. You can proc it pretty well with your E>W combo, but this can be pretty inconsistent. The real fun begins when you get Rylais's, which I usually get second item. Since your plants will now apply a slow, cheap shot becomes MUCH more reliable. With a cooldown of 4 seconds, I generally get about 3-5 Cheap Shot procs in a single teamfight. That really adds up...
The third rune I take is generally Eyeball collection. Who doesn't love damage? If you're not playing like a baboon, you should be able to stack it pretty reliably. If you're kind of behind, grab a lens trinket and hunt down wards in river.
For my final domination rune, I take Ravenous Hunter. Zyra has no innate sustain, so this helps a lot. PLEASE don't quote me on this, but I'm ninety percent sure that her plants also proc Ravenous Hunter. Additionally, being single target, they should give the full healing amount.
For sorcery, I go Manaflow band into Gathering Storm. Manaflow band helps me spam my abilities in lane, while Gathering Storm helps me scale even harder. If I'm REALLY trying to be greedy in lane or if I'm up against someone who I absolutely cannot let farm, like Kassadin, I might take Scorch to add a bit more poke. Manaflow can be subbed out too to be honest, as she doesn't really have mana issues, especially after getting lost chapter.
For Summoner Spells, I almost always take Ignite because I'm a greedy motherfucker. I've rarely had games where I regret taking it. Teleport, exhaust, barrier, heal are all decent/situational alternatives.
for shred. Her plants also have high range. I want to get good with her so I can 
mid is also annoying as hell.
mid is annoying as shit too.
