If a character with 90 hit points ends the day with 1 hit point, she will have 90 hit points again assuming she gets a good full night's rest. You might want to argue that a character hurt that bad must have a broken bone or deep cut that would take much longer to heal, but we have been ignoring that game mechanic since the inception of D&D anyway. A broken bone would more likely manifest itself in a penalty on to-hit rolls or in limited movement. But, like I said, this is fantasy. If you want that sort of realism in the game there are no reasons you cannot create your own house rules to cover it.
In the 5th edition your full resting period is called a "Long Rest". You can only have one "Long Rest" per day and once you have completed your "Long Rest" you can regain all your spells and many other features are reset as you might expect.
The 5th edition named this a "Long Rest" to distinguish it from a "Short Rest"; another new feature players will enjoy. A "Short Rest", page 67, is a period of downtime that lasts at least an hour, and you can have several "Short Rests" each day. There are two actions characters can take after a "Short Rest" that I will mention here. One, found on page 31, is called "Arcane Recovery" and allows arcane casters to recover spell slots equal to half your caster level. The other action allows any character to recover hit points. You roll for the number of hit points recovered. You can roll the die you use for gaining hit points when you level up (your hit die), and you can roll it once for each level. Thus a 3rd level rogue that rolls d8's for hit points could roll 1, 2, or 3d8 to recover that many hit points after a "Short Rest". Short rests should allow our characters to stay out in the field adventuring longer before heading back to the home tavern.
Page 67 Long Rest and Short Rest