For dungeons, you can effectively heal as a Sorcerer, while for trials, it's a bit harder to support as a Sorcerer.

Dungeons:

There's no way around it though, Sorcerers are very poorly optimized for contributing DPS in a fight, while keeping up healing of any kind. If this were a Templar, you can load them up with cool dps spells because they have them; Sorcerers don't have anything to put into spare slots.

Basically, in a boss fight, you'd throw down HOTs and DOTs, and then swap to Overload, spam that before you only have enough Ultimate to use Warhorn, then buff yourself with Surge, then swap to Resto Staff and use Warhorn, then continue healing. If you run low on Magicka, you'll have ultimate, so swap to Overload, then Dark Conversion.

Also, you need to heavy attack with Resto Staff for Major Mending, which is a necessity.

Keep up DOTs, and keep up Combat Prayer and Empowered Ward buff. You have almost no way of contributing DPS, so you need to keep Combat Prayer up to maximise that.


Trials:

As a Sorc Healer in a trial, flat out, you are dead weight compared to a Templar. But still, it's something you can do. First things first, coordinate with your other healer, which hopefully is a Templar, if not, your group is going to have resource problems.

Right off the bat, you need to insist that you will take all of the abilities that the healers trade off on, all of them.

So, your setup should look as:

To ensure that the Templar has plenty of room and time to cast all the stuff that 2 Templars normally has to do, you need to run Siphon Spirit, Mystic Orbs, and Elemental Drain. But just like a Templar Healer, you'll buff everyone with Regeneration, then keep down Healing Springs, and use Combat Prayer as your buff/main heal.

Also, you need to keep up Empowered Ward buff at all times.

As with a dungeon boss fight, you'll open up with initial HOTs + Overload, but modified a bit. First, communicate with your other healer and tank, and make sure one of them opens up with Warhorn, so you can burn your ultimate until you have just enough to cast Warhorn. So, again, burn ultimate, and rely on Matriarch as a healer. Then, use Surge before you swap back to normal bars, then cast Warhorn when the time's right.

You need to get ~90% uptime on Siphon Spirit and Elemental Drain on as many mobs as you can, and a similar uptime for Combat Prayer. If you run low on Magicka, swap to Overload and use Dark Conversion, buff with Surge, and move back to normal bars.

You don't have the utility of a Templar, so you need to try extra hard to do a ton of healing and buffing. Keep Major Mending up via Resto Heavy attacks.


You should still run standard 5 piece SPC as a sorc healer (if you have it) + Worm Cult (in trials, if you have it), or + Infalliable Aether. If you don't have any of those sets at all, then I'd advise you to make do with Julianos, Willpower, and a monster set (preferably Kena). Even with the low sustain setup of Julianos, 2 Kena and Willpower, you have an easy way to restore Magicka.

You'll need a bit of practice before you can get it down, but once you do get it down, it'll turn out nicely.