As a support Zyra main I feel that I should address some of the misconceptions, and provide some advice here.
The first thing I keep hearing about is people maxing Q for damage first. This might have been great back when SKT won worlds with her, but her oppressive damage and range was toned down a bit (rightfully so). Today's Zyra should be using E as her main damage ability. Rooting the enemy and dropping snare plants around them not only does huge damage, but sets up your teammates to dive on them and often still slows even if the actual roots miss.
Second, regarding the difficulty of landing spells, you shouldn't be expecting to play her as a blast mage like LeBlanc or Lux. I'd argue that Zyra is more powerful than either of them, but trades off a lot of speed in exchange for one of the strongest skill sets in the game. One very effective way to play her is to react to your opponent's moves rather than trying to catch them out of position. Did the opposing Leona catch your adc? Drop E/seeds in front of their adc so even if they dodge back to escape it you've now isolated Leona for easy pickings. If they aren't watching, or are too confident they can take it, they'll get a rude lesson in just how much damage you can dish. Try catching them off guard by hiding around corners or in bushes when you know they're coming. Get boots of mobility to help you find the right positioning and outmaneuver enemies. Use flash offensively to jump on enemies who think they're at a safe range from your roots. >Learn to combo her spells quickly< You can drop everything she has in less than a second, and when you land that on a hapless foe, you will often just insta-gib them right there. Of special note on that point, the huge majority of her damage is AoE so if you can tag multiple enemies in the center of your dump, they will all be rooted, knocked up and low health for easy clean up from your team (in one special game where I was fed, I actually managed a penta kill in just a few seconds when I caught them from a bush). The combo is also a great way to respond to the enemy team engaging, often turning the tide of a battle instantly as the other team is more focused on landing their abilities than dodging yours.
Third, people seem to think only about how easily her abilities can land. Now there are many ways to make that happen, as explained above, but Zyta is also really strong for zoning enemy players. Dropping e/w between enemy champions can isolate individuals for your teammates to pick off. R can break up the enemy team and ruin their engage by forcing them to choose between being vulnerable to a strong counter engage or backing off and leaving several of their allies in a very dangerous position. W is also an amazing tool for scouting, with a huge range it can check bushes before you're close enough to get jumped, or around corners/over walls to try and find hidden enemies.
Lastly I just want to say that I consider her to be easily the strongest support in low-mid elo soloq. When you can't really count on your adc, it's great to be able to put out large damage while keeping a safe distance during lane phase.