You can’t see at all in total darkness in DnD 5e unless you have darkvision or some other feature that allows you to see in darkness. That’s because darkness creatures a “heavily obscured area.” Any creature in this area effectively suffers the blinded condition, which causes you to be unable to see and automatically fail any ability check that requires sight.
Creatures with darkvision can see in darkness as though it were dim light. How far they can see depends on the specific feature.
Most racial features, like for elves and dwarves, allow for the creature to have 60 feet of darkvision. Likewise, the darkvision spell allows for darkvision out to a range of 60 feet.
Some races, like drow and duergar, have 120 feet of darkvision, meaning they can see 120 feet in darkness as though it were dim light.
Note that creatures with darkvision can’t discern color in darkness, only shades of gray. Additionally, dim light still gives disadvantage on Wisdom (Perception) checks, so even creatures with darkvision can’t see well in total darkness.
