There's a few ways to level a char with RoS, including story, but no one plays the story more than once cause it has shit density and stupid unskippable scripted events all over and shit like that. Mostly people do rifts, randomized dungeons with a rift boss at the end(either variations of existing story bosses like Rakanoth, or original bosses). You can also level doing bounties if you prefer, which are like quests, you get 5 per act, generated randomly from a pool of like 50-100 per act or whatever the actual number is, generally are like "complete x event" or "kill this rare + x amount of mobs in the zone". Complete 5 and you get a box with some bounty only legendaries and shit like crafting plans, bloodshards(currency to gamble on legendaries) and legendary crafting material to use in the cube/craft legendaries.
Both fall under adventure mode, which is like the story world, but not split per act, you can move freely to any zone on the map and farm anything, do the bounties there or open a rift in town.
The main issue is most of the good features in the game are RoS only by now. Playing vanilla feels kinda like shit. Less shit than it used to be, arguably, but still kinda shit.