overwatch
Zenyatta is a low HP, support class character. I understand the basics of his abilities, using the discord orb for damage amplification, using the healing orb to support my team, and that his attacks are fairly effective from long range.
What strategy will help me play Zenyatta effectively, using his skills? He feels very different from the other support classes.
Shoot the ground directly in front of the opponent. Since its a scatter effect it will work best against big targets. It's a little tricky to do, as the idea is that the arrow will impact the ground so close to the opponent that all the scattered arrows don't have a chance to go into anywhere else. I would recommend loading up the training grounds and trying it on the training dummies to get a feel for how it works.
Edit: Here's a crude drawing of what you're trying to do. The red line is the scatter arrow. It's like you're firing a shotgun shell at the point of impact so the closer the impact point, the more effective it is.
Turrets: these seem pretty strait forward but can actually be used in a variety of ways. Obviously the most strait forward is to cover choke points. This is extremely effective IF you can place them in such a way, that is inconvenient for the enemy to have to destroy. For example, if you place turrets above the enemy, on to your side of the wall, when they walk through they are forced to look up to shoot it. They are using that time to look up to shoot the turret and not your team. That's a minor victory in my book. How I like to use the turrets however is a bit different, and I'll tell you why. Symmetra gets notifications when her turrets are attacking, or when they get destroyed. I generally place 3 at the choke point if I'm defending, and I'll place the remaining three around the area where sneak attacks are common. This allows me to spot the attack well ahead of time and warn my team mates. Do not under estimate this, it's extremely useful. Also they slow, so there is that. I should also note that the turrets can be placed ON payloads, so when attacking you get mobile turrets, which can be nice. (I don't cover turret placement itself very well here, that's a topic in and of itself. however there are good tips from other commenters below)
Don't hesitate to read the Reddit post, you have many more information about the rest of Symmetra's kit and the synergy between her abilities !
Best Answer
Zenyatta does have a somewhat unique playstyle. His squishiness makes it so he needs to stay out of the open and stay near his tanks, preferably a Reinhardt who can use his barrier to shield Zenyatta and help make up for the squishiness.
Zenyatta's orb of Harmony heals 30 health per second, which is lower than Mercy's healing, but has a longer range, as an orb of Harmony will remain on an ally so long as Zenyatta has line of sight of that ally. One thing of importance is that Zenyatta cannot send his orb of Harmony through an enemy shield or barrier. Generally you want to throw this on whoever is taking the most damage, usually an offensive or tank hero.
For orb of Discord, this like orb of Harmony can be thrown at a range of 40 m, and remains at any distance provided that he keeps line of sight. Orb of Discord provides 50% bonus damage from all allies against the target with it on, so it is good to put on the enemy tank to help burn them down, or on an enemy offensive hero to make sure they die quickly before getting damage out. Note, losing line of sight for 3 seconds will remove the orb, and it cannot travel through enemy shields and barriers.
Zenyatta's regular attack does quite a bit of damage (35-175; 35 per orb in charged shot and 5 shots total; regular fire deals 45 per orb), especially if you have an orb of Discord on the target. His charge shot is great to use when ever someone gets close range and needs to be killed as quickly as possible such as a McCree or Reaper. His regular fire is great for wearing down the enemy from a distance, though it does have a travel time, so make sure to lead a little. Times when you should charge his alt fire would be, when McCree uses his ultimate Deadeye, when Reaper is Shadow Stepping at a destination, when Widowmaker is sniping in the distance as you want to not expose yourself to snipers, while Mei is in a Cryo-freeze (fire once she unfreezes), when Zarya's barrier is on someone (use it when shield wears off). You can also use it to help burst a Bastion or Torbjorn turret by charing in cover and popping out to unleash all 5 orbs at him.
His ulti heals for 100 health per second to nearby allies and makes him invulnerable to damage for 6 seconds. While using his ult, you can block a number of enemy ults from hitting your team such as Blocking enemy ultimates most notably: Reinhardt's Earthshatter, D.va's Self-Destruct, Mei's Blizzard (the line of sight starts with Mei's Blizzard Drone), Junkrat's Rip-Tire, McCree's Deadeye, Reaper's Deathblossom, Pharah's Barrage, Bastion's Tank Form, Roadhog's Whole Hog. The main uses for transcendence are for initiating strong pushes, to simply save yourself, to counter pushes done by the enemy, and to massively heal your team.