I'll second Rift. All the game modes are different, but Rift is probably the most in-depth and representative; and if nothing else, Rift is what primary balance and design focuses on.
I'll also third not worrying about it too much and just playing.
If you do want specific advice, though, I would mention the following:
Lanes/roles. Dota didn't, at least as far as I saw, have much of a meta or structure to it, beyond some people insisting they got solo lane. LoL does- each lane is typically expected to have a certain type (and number) of champions in it. Exceptions exist, but the following is what usually works out:
Top lane is a bruiser of some sort. Actually, a lot of ranged champs that bully bruisers are popular now, but traditionally someone somewhat tanky and with good mobility usually went top.
Mid lane is a mage. This is partially because the lane is shorter and thus it's easier for slow, squishy mages to flee back to their tower, partially because you want a magic damage dealer on the team so the enemy can't stack armor, and partially for other complex reasons.
Bot lane is a ranged AD carry and a support. A ranged AD carry (adc) is someone squishy who deals monstrous damage when they get enough items (somewhat equivalent to ranged Agi heroes in Dota; melee carries are kind of risky and thus not typically used). A support is a character, usually an initiator, tank, or someone with healing or other buffing skills, who leaves all the tasty minions for their carry to get, and is basically in charge of babysitting them so they can grow up to become monstrous.
Finally, you have someone in the jungle. They eat jungle creeps, then come around and gank lanes, hoping to score their team some kills and breathing room. Especially in low-level play, this sometimes gets passed over and two people go top, to varying degrees of success.
Oh, and if you're coming from Dota I'd guess you're aware of this, but pay the ragers no mind. If they knew what they were doing they'd be playing or advising you instead of sitting there screaming insults at your mother. And, as something of a corollary, try not to get upset yourself.