In the beginning you should run 2 Tank, 3 Heals, 7 DPS because your healer and tanks need pratice (especially on Sanctum, tank might die easily lol).

When your group gets better you can go 1 Tank, 2 Heals, 9 DPS in all the old ones, you still need 2 tanks in vMoL.

As far as skill go idk, DPS has to pull numbers, the higher the better, for leaderboard runs you need people that pull 30k but for starters 15k is okay. There are some really good builds on Tamriel Foundry for each class so there's no reason to go into the details too much.

Tank has to use War-horn, has to have decent gear and needs to know how to stand (some tanks spin around dungeon bosses while light attacking... most trial bosses cleave and you don't want to wipe because of that...)

Healers have to use the horn too, you want them to use Spell Power Cure and go Destro\Resto.
They have to use Syphon Spirit, Element Drain, Mystic Orbs and Blazing Spear if they are templars for the team resource managment. Forget about breath of life, they should heal with Healing Springs and Rapid Regen most of the time (+points if they have a Master Restoration Staff).

Just wanted to add my 2 cents.

I don't generally competitively run Trials but it doesn't sound like you want to go for the leaderboards so perhaps my advice will come in handy. Old Trials(can't say anything about MoL, haven't bought TG so never tried it) are really easy now, the biggest thing isn't group composition but group coordination. Perhaps your people will be missing out on some cues and taking a lot of damage and you'd need 3 healers rather than 1. That's okay. The dps checks are easy enough to be done with just a handful of dps now so see for yourself. One thing you should really look into before starting a run is mechanics(and how to explain them to others which can be a bit of a pain sometimes).

My limited Trials experience says 1 tank 1 healer is enough for all 3 old Trials. Granted I've gotten my SO clear with 7 people lol(that's not because I'm OP like that, that's because I don't feel comfortable around big groups most of which I don't know, I'd honestly much rather wipe with a handful of chill friends and learn how to manage it with ~4-7 people. Makes for some extra challenge too). Imo it's actually easier with <12 to a point because less coordination required, no orbs issues on Serpent, no mines everywhere on Manti. We had 1 tank, 1 healer with offps, 1 sorc-that-kites-Manti-when-others-go-down(that's me! XD) and the rest was pure dps. ...I don't advise Manti kiting though lol, it can be fairly complicated. So suppose 2 tanks 2 healers for SO. Generally though, start with a tank and a couple healers perhaps and see how it goes for you.

Good luck!;)

Also, if you're NA PC I can run with you or perhaps recommend you a nice guild or two:)

EDIT: Classes are not THAT important anymore, unless perhaps for leaderboards. DKs are convenient to have because of chains(to pull ranged ads in where they can easily be AoE'd). Templars are great for shards/repentance(not to say you can't heal on another class, just make sure your tank either doesn't have stamina issues or is getting shards from someone). If you struggle during high-damage phases, keep in mind some ultimates reduce the damage the group takes, such as Nova and Veil, so those are good to have.

I'm on Xbox NA. Most of the people I play with are either pvpers or really bad pvers.