Right now, and even through most of the VR levels, you can play what I call a "dumb healer". There are essentially two skills that Templars can use to keep a group alive through almost anything:

Healing Springs (morph of Grand Healing, Restoration staff)
Breath of Life (morph of Rushed Ceremony, Restoring Light)

Healing Springs is the main heal, because it's cheap, range castable, and spammable. Breath of Life is the "oh ****" button. Just with those two skills, people will think you are a master healer. Seriously, no joke.

However, if you want to be a "smart healer", there's more you can do:

-I believe that everyone in a group should contribute damage, even if it's paltry. You're a Templar, so you have Radiant Destruction, a powerful ranged execute (use when enemy is at 25% HP or less). You can use it as a normal attack if you want, but it hits much harder at low health.

-You can further your damage dealing with Backlash. It's cheap and casts quickly, so you don't waste time using it. It stores up damage on the enemy it hits, and casts a light on them, which I think makes the target easy to see. After 6 seconds, it explodes, dealing damage. The only caveat to using this is keeping it up, and managing that with the rest of your skills.

Beyond healing and damage, really good healers will provide further support:

-Spear Shards will many times be requested from you in high stamina situations for the tank. It gives stamina to whomever picks up the spear, except the caster, who can't.

-Repentance (morph of Restoring Aura) should always be on your bar, IMHO. It's a free heal that also gives back stamina. Stamina based DPS members will love you for it, as well as the tank, plus it saves you from needing to use magicka.

-Siphon Spirit (morph of Force Siphon, Restoration Staff) is an excellent way to passively heal and return magicka to players. It has a 1.5s cast time, which is inconvenient, so it's mainly useful for bosses.

-Combat Prayer (morph of Blessing of Protection, Restoration Staff) is a nice way to increase your groups damage output. I'll admit, it's tough to keep this up on members because the range it hits is small. I slot it if I need, but I'd rather sacrifice it for something else. That said, the heal is decent, and I've seen a Sorcerer healer use this to burst heal our group during the final boss of vFG.

Passives:

Every single passive should be unlocked, eventually, for any skill tree you use. Healers, DPS, tanks, doesn't matter. They're all good and worth it, though some more than others. Cycle of Life, for example, from the Resto staff line will help you with magicka sustain. Focused Healing, from Restoring Light, will make your Templar heals hit harder.

Other skills:

-Inner Light (morph of Mage Light, Mage's Guild) should be on and slotted on both bars. This is done mainly so it never turns off when you swap bars. It increases your spell critical, meaning your heals will crit more often, and increases your max magicka, which will make you heal more. If you can spell critical in a different way, then by all means you can. Inner Light is just the standard way it's done that everyone has access to.

-Cleansing Ritual (Restoring Light) should always be down, IMHO. This skill hooks into the Focused Healing passive I mentioned before. When allies stand in Cleansing Ritual, your heals will do more, so keeping it down and around where the fight is happening will help you heal better. Plus it passively heals, AND it gives group members a way to cleanse negative effects on themselves.

-Nova (Dawn's Wrath, ultimate) would be a good ultimate to slot. The reason is that enemies do 30% less damage when they're in Nova. It's an expensive ultimate, at 250, so you have to save up to get it. I typically slot Meteor (Mage's Guild) as a primary damage dealing ultimate because it costs 50 less.

-Remembrance (Restoring Light, ultimate) is an excellent secondary "oh ****" button.

Things to consider:

My bars do change a lot, depending on the situation and the skill of the players I'm with. However, in general, the skills I listed above are on them somewhere, or I will put them on if needed. When I heal, I don't bother with close range attacks (Puncturing Sweep, Empowering Sweep, etc). Staying that close to a boss or a trash mob is a great way to kill yourself. Instead I focus on long range and the job of being the glue that keeps the team together. You are the common denominator, everyone relies on you. DPS don't typically care what other DPS are doing because it doesn't matter. Tanks just need to know that people are doing their jobs because it's hard enough soaking up the damage some endgame bosses can do. Healers have to see everyone and everything.

Of course, you can't run around doing quests/content while only healing, so for that you can swap in Aedric Spear damage skills, or get a Destruction staff and Force Shock/Impulse things down.

As for attribute points, I would focus on having magicka for now. At VR14, the current meta is that DPS and Healers should have ~20k HP. How you get there doesn't really matter, and many players will forgo almost everything that increases health, then eat green quality HP food to boost only that stat. I typically place all my points into the thing I will use the most. Stamina DPS? All points in stam. Tank? All points in HP. Healer/magicka DPS? All points in magicka. You can make up the deficit by enchanting armor with health, getting jewelry with health, and of course eating your food.

Holy crap, that turned out to be a LONG post. I'd have put a "tl;dr" but it would just make this post even longer. Hopefully there's enough here to get you going.!