It sort of depends how much time you want to devote to it. Essentially, you build different rooms in your vault and assign dwellers to work in them. Those rooms will produce energy, food, water, stimpacks, or rad-away for you to use, depending on which ones you build. Your objective is to keep your energy, food, and water levels above the required amount to keep your vault running. It's not turn based at all.
As you train your dwellers to specialize in the various work rooms, you can also gear them up to go on quests or send them into the wasteland to look for caps, weapons, or outfits. The quests can be fairly intriguing, but they're nothing super time consuming. You send your team on a quest, and it takes them anywhere from and hour to over a day to get there before you can play it (as with most free games, you can put money into it to speed things up), but if you're a casual player, you can just send your dwellers on their way and check back on them later to wrap up the quests.
I've put maybe 10 hours into it, but I leave it running sometimes while I do other things. Your vault keeps working even when you're offline, so you don't need to worry about things crashing and burning if you're not online.