O Hai I'm OlldGregg! Wanna play some lovegames or drink Bailey's from a shoe? I am a gold division player who mains as zyra support/mid. I am not saying I am pro, but for anybody from silver up to gold, this build is solid and compliments virtually any team comp.
The major concept behind this build is to always buy wards, to rely on masteries/runes for damage, and to build tanky so as be able to bait like a boss and still have an initiate THAT IS OVER 9000!

As support I want to ensure that my adc can farm without pushing the lane, fear of being ganked, and poke my opponents in order to prepare for a kill. I will always ward their front bush once the lane phase begins and dragon/tri-bush shortly after. Hopefully once those wards expire you can afford a phil stone and are just about to hit 6. Go buy and then have your opponents feel the wrath of level 6. If you haven't done a defensive exhaust yet, save your exhaust for the enemy adc if you land a root with 2 plants. If it works, chuckle, rinse, and repeat. Zyra has an ult like has true wombo combo potential, like partnered up with the MF ult, so let the snowballing begin.

Once you are level 6, you better have a ward on dragon at all times. After phil stone, either get kage's pick or sightstone, but preferably sightstone. The only reason to get kage's is because you can't afford sightstone. Until you buy a sightstone, try to always have 2 wards on your person. Control dragon with wards! Once you have those 3 items, boots and aegis are your next two priorities and twin shadows is the first core item you want to finish. From this point on as long as you can do your combo, the cc is sufficient to give a major advantage in any teamfight. Late game items include zhonyas, rylais, twin shadows, and sightstone.

Whenever you land your root and you have your adc next to you, DO IT. For major teamfights, I consider it a missed shot if I don't capture 3 of them, but wasted flashes are just always good. Also twin shadows is one of the best synergistic items for zyra because once you late your ult, you are set, and twin shadows just makes this too easy.