Drop Morello's from your standard build. FQC, Boots, SS, Liandry's, Rylai's or Guise, Rylai's then Liandry's depending on whether you think the slow is going to outweigh the tank HP burn. Consider mobi boots for their roaming power. I usually get Frostfang first, then mobis then finish the build unless we're behind and I know I won't be able to roam.
Level W last, especially with the recent changes to her in the last patch. Personally I prefer to max E as support with 1 maybe 2 points in Q. Midgame your root duration is going to be your key utility.
When you kill your lane early and your ADC inevitably starts to back if you know or have a good idea where the jungler is then ping the tower and push the wave hard. Getting bot tower first is a pretty big advantage.
Other than that the other posts cover it pretty well, press the advantage by taking tower after tower.
The one big thing to keep in mind with Zyra specifically in mid-late game is that since you KNOW that your team will always overstay like every team does use that to your advantage. Even if you see some opportunities to get in some good poke at the tower Zyra's real strength is in the disengage/re-engage. Save at least 1, preferably both seeds and your roots for when the enemy team comes charging down let your team's retreat bait them just long enough for them to get strung out a bit then root/seed/ult the front line. Most times this will be enough for your team to turn, kill them again and maybe even go back and finish off the tower/inhib, worst case scenario you get a good disengage and save them from getting wiped for overstaying.
I'm sure you've seen that last bit play out over and over and those are probably the moments when you see your lead fade away. IMO Zyra is one of the strongest champs at preventing this if you plan ahead a bit and save your resources.