Well, templars are great healers (even with the nerfs coming in Morrowind) so you got that part right for sure Far as skills go, you can definitely do most dungeons using 2-3 skills(hell one even) but doing so means you're missing out on most of the options open to you. On my templar I tend to struggle because there're so many useful things I want to put on my bar yet only 10 slots!

Useful skills for a (templar) healer:
- Healing Springs(Resto staff first skill) - listing this first because this is THE heal, spamming which you can get through most content and never die. It should not be the only button you press, but it's insanely cheap, it's aoe, it stacks with itself, it can be block cast. I find it often underused by templar healers in favor of BoL, it should not be. It has the upside of being spammable, being aoe and actually(in my experience) hitting the target faster than BoL does.
- Breath of Life (restoring light first skill) - best burst heal in the game. It is not to be spammed, it's there for emergencies.
- Purifying Ritual (or whichever morph, same skill tree) - a weak HoT and a cheap cleanse, a must for certain boss fights where you need to cleanse certain harmful effects. I personally don't always slot it.
- Combat Prayer(Resto staff again) - great burst heal, great damage buff, you want this on your dps as much as possible
- Shards(Luminous Shards or Blazing spear morph, either works I think, Aedric spear skill tree) - actually decent aoe damage but its main use is restoring stamina to your allies, usually the tank(since stamina regeneration completely stops while blocking now it's all the more important)
- Orbs(last skill in Undaunted skill tree, both morphs have its uses) - one of the morphs is great magicka support, the other a pretty decent heal(with some minor magicka restore still)
- Elemental drain(destro staff) - great magicka management help for magicka dps, pretty much a must if you have any in your group
- Repentance/Radiant Aura - Repentance is a free heal and stamina restore from dead bodies(which unfortunately will no longer restore stamina to group after Morrowind, severely limiting its usefulness), the other morph is the same thing as Drain basically(they do NOT stack)
- Channeled Focus(last skill in I forgot which templar tree, you'll find it) - armor buff, healing buff, free magicka regeneration(quite a bit of it too). There's no reason not to run this unless you're really out of bar slots
- Annulment(light armor active skill) - it's not a heal and won't directly help you with healing but it will save you from getting one shot and being unable to heal group because dead(most healers run 5+ pieces light armor and 17-20k health, making us relatively squishy); one of its morphs restores magicka when absorbing magic damage too, making it free to spam in most fights. It's not a must for most fights but I always run it on backbar just in case.
- Inner light(mages' guild tree) - if you're still somehow suffering from excess of skill slots ( ), this will passively buff your max magicka and crit rating, thus making your heals more powerful

If you still have free slots, no reason not to add to your group's dps too - long as you're still keeping track of everyone's health
- Jesus beam - Radiant Destruction - is a very powerful execute, it's used by healers a lot outside of extremely damage intense situations. Becomes useful somewhere under 40% of enemy's health.
- Puncturing Sweeps is a nice aoe damage, but it's melee range and is a channel(as well as Radiant but that one is at least ranged) so be careful if you slot that. You can block cancel it to emergency heal but it's still not instant.
- Wall of Elements from destro staff skill tree is not just nice damage, both single and multi target, but if you use the lightning one it'll greatly buff your dps' damage by setting the targets off balance and proc'ing a certain champion point passive. It's mostly relevant for endgame so I'm just throwing this out there for possible future use, don't worry about it too much.

...I feel like I've written enough of a wall of text for one time Hope this doesn't overload you with too much info, a lot of this stuff is really most relevant for endgame rather than your average pugged dungeon, but this should at least give you some idea of what other skills you could use as a healer