I've played TT since season...1? Basically, since TT was called TT.
That said, the new TT has a much different feel than the previous one. You could follow this formula and win most of the time with decent teammates until you get to higher-level ranked play:
Get a bruiser, a tankier bruiser, and a high-cc mage on your team. Send your bruiser up top, have him capture the altar (while being watched, in case of 'contestation') or grab golems between wave clears. If he's having problems going against the enemy top, have him sit under turret, clear waves asap, take golems/altar. If he's doing well against the enemy, have him clear waves in the middle, then retreat, doing the same. He should be able to get enough gold by level 6 to be useful to the team (a couple lvl 6 strats incoming if you scroll down a bit).
The other 2 ppl bot, having the mage grab most of the cs gold, poking enemy (if they have 2v2 bot, just poke, if 2v1, pressure). After each wave, until around lvl 6, have your tankier bruiser check jungle camps to make sure there's no invade, and help with altar, etc. At lvl 6, have him shift to jungle, ganking whichever lane EVERY JUNGLE CLEAR.
After lvl 6, every 3rd wave/clear or so, your team should be organizing counter ganks as a team, or taking altars and forcing fights where YOU want to fight. Bush camping, invading jungle, whatever. Just make sure you are in positions that one of your guys won't get cut off from the other 2. That's easy to do on 3v3.
After lvl 14, your strategies should shift to forcing enemy positioning away from a minion-pushed turret. Your objectives are easier to manage with altar buffs, but you don't need them as much if you have smart team play. If you can manage to take 1 inhib, while keeping at least your inhib turrets up, you should win. If you do this without wiping in the process and are able to regroup, a loss at this point would mean you should switch back to SR or get better teammates.
Ranked play is similar, but there are different early-jungle clear strats, full-team roaming strats for early game, etc, that Gold teams do, claiming that if you don't have such strats, or a full-time jungler, you won't ever be competitive. From what I have seen, although I never have been able to find consistent teammates for 3v3 ranked, I would probably value early 2v2 or 2v1 bot lane and shift into the fulltime jungle strat later. It's just as effective if you clear waves quickly and clear jungle camps together in-between, and I feel it defends against invades a lot better. It also forces all team members to be aware of what's happening in the jungle, making it easier to assist other lanes as well, and ensure altar buffs. But that's me, I guess...