Default assumptions in the PHB have always worked for us. 3 failed death saves and you're done, but there are some options for bringing characters back, so long as you have the financial resources and access to high level spell casters. In our 5e games, nobody has followed through on the option to revive, with maybe a half dozen PC deaths in campaign play. (Most of our character deaths are in one-shot adventures where DMs and players are less careful. And I could see us handling the resurrection of a character killed in a one-shot entirely narratively, as there are recurring player characters who get leveled up and down appropriately when we need to do a one-shot in a hurry.)
We had one instance where a player was pretty upset to lose a character and kept reminding the DM, "you're the DM," which, I think, meant, "You can make this go away." He didn't ask us to try and revive the character, though, so...
As a DM, I would be cheesed by a player who insisted on just "bringing a character back" on the spot. As a player, I would be cheesed by a DM who, after a PC death, announced that, no, actually, there is no resurrection magic in this world and, even if you have the GP and know high-level casters, it's just not gonna happen, sorry. (Fine to set that out in a session 0, and more than fine to put some sort of quest or challenge in the way, but not great to just close off that avenue entirely after the fact.) We don't ever discuss revival in session zeroes, but we do discuss the intended level of lethality. Should PC death be something that players have to willingly walk into? Should PC death be constantly just around the corner? Or something in between? We usually settle for something in between.