There were some timekeeping approaches, including candles marked with the hours based on burn rate (also used as alarm clocks by sticking metal things in them that would fall on a bell or metal dish below), but there also wasn't a lot of reason to know the time accurately at night. Hell, in the time before clocks, there wasn't much need to know the time accurately in the day. People used sunrise, noon, and sunset as the major markers.
They didn't. They went to sleep shortly after dark, woke up around midnight to fuck and eat, then went back to sleep until dawn. For hundreds of thousands of years.
The stars have a very predictable pattern to them, ancient people had nothing better to do at night than look up, and since there was no light pollution it was quite a show.
Depending on the time of year, some constellations would be visible all night and move across the sky. That's where the original Zodiac signs came from.
They actually didn't for the most part, hour level divisions were mostly for the sake of tracking time in the daytime, when having that level of precision could be important for things like jobs or time sensitive tasks, but at night all that really mattered was that you got to bed with enough time to get a full night's sleep.
Precise time came to humanity with the railroad. Until then no one cared very much about whether it was 11:35 PM or "around midnight" or "way past bedtime." Train timetables were the first thing that made minutes matter to the general public.
Mariners cared about time and preferred to be as precise as possible, but did pretty well telling local time by the stars. Finding longitude was a problem until good clocks came aling though.
So I got scooped on the whole candle thing, which I really wanted to go with. Instead, I’m going to pivot and say that accurate timekeeping - day or night - was actually driven by the needs of navigation. 
You could get a pretty good idea of when it was based on the position of the sun and stars, as long as you knew where you were. The opposite is also true - you could figure out where you were, as long as you knew what time it was (and had the appropriate charts/data). The problem was that, while sailing around the world, ships often didn’t know either one.
For rough purposes, people used things like candles. In some cases, monks would recite specific prayers at a given cadence to keep track of time overnight and so know when to wake the others. These methods, as well as later inventions like the pendulum clock that used a known time component to drive watch mechanisms, were all but useless for navigation due to inaccuracies. They were good enough in the 1200s to let the monks know when to pray, though.
An amusing way people used to wake up early was by drinking extra water before going to sleep. Their full bladder would wake them in the early morning hours (unless they overdid it, in which case they had to use the potty in the middle of the night and then overslept).
Animal noises. Most people had animals or lived near other people with animals, so the morning hours had a bunch of typical animal noises (animals, like humans, have an inner clock, and some animals are programmed to wake up before dawn).
Logs near the stove. A seasonal thing, but in winter, if you know you usually refill the stove 3 or 4 times during the night, you can tell how much of the night has passed through your wood stack.
The bi-phasic sleep thing also helped (take a good nap around noon, but also wake up at midnight and drink a beer with the neighbors). The point of midnight may have been rather arbitrary, though.
As far as I'm aware, candles were affordable, but the average person still couldn't afford to burn down a candle every day to work or measure time, so once it got dark, normal work ceased and, at best, a family would meet in front of the stove and tell stories, knit or carve for a while.
Moon position, it's not as reproducible as the sun, but you can really see the moon moving through the sky.
Light, especially in summer, it starts to get night around 22, is pitch black at midnight around 3-4 you start to guess some light in the sky, at 5 it's not day yet but you can see without a torch, and at 6 it's bright.
Candle and fire-pit aren't objective clock, but still a way to evaluate how much time has passed.
Water clock was a possibility but uncommon. Early industrial age was a person that you paid to come bang on your shutters until you responded.
Most people just kept a circadian routine. Another trick is to simply drink as much water as you need so that you will wake up after a given amount of time.
The idea of time as a unit of measure that is critical for task completion is a rather new invention of current culture.
THE Big Dipper's angle can be used to tell time at northern latitudes. It stays in the sky all night. I was told by a Blackfoot elder that they used it as a clock on clear nights.
The position changes with both time of night and time of year. Regular observers can tell time by the angle the constellation sits at.
Oh hey! I actually read into this recently. It came from wondering what exactly "The Witching Hour" was, and apparently it was invented by Christians and it's between 3am and 4am. I thought "oh hey that's interesting when did that start?", and then when I read that it may have started back in 1535 I was like "Wait how the fuck did they know it was 3am in 1535? When were clocks invented?!"
So then I was like "well how did they tell time at night before that?" and it ends up that all the way back in the 16th century BC, they had these things called water clocks. So basically, they had figured out the sun dial a few hundred years before that, and while tracking an hour, they had 2 vessels, one full of water and the other empty. They would have the water flow from one to the other so that when the top vessel was empty, x amount of time had passed (for sake of simplicity call it a hour), then they would pour the water back into the top vessel to measure the next hour, and they were able to do this without the sun. It was basically the same concept of an hourglass (which actually didn't come around until 1000 AD) but with water.
And before sundials and water clocks? I dunno. I guess they just went to sleep when the sun went down, and woke up when it came up, and didn't plan things around specific times. Sounds pretty nice, honestly.
Star movements probably. They also knew how long certain things would burn for. There were even candles that would be marked specifically for hour counting.
some towns hired people to wake the town for work, and someone else would be hired to wake them up. some societies studied the stars and moon to tell the time at night. and like others stated, there were candles, lanterns, and furnaces to tell how much time has passed. people were more in tune with their environment
Just spoke with a tour guide about this topic. If you lived in a city during the middle age in Europe, the night watch announced the current time every hour. How did they know the time? They just guessed, because nobody in the city could know better.
Not sure how accurate this is, but in The Name of the Rose by Umberto Eco, some monks stay up all night chanting so that they can wake up the other monks for morning prayers. So, the night monks chant a Hail Mary X number of times, and that takes them Y amount of time.
By analyzing how the values on the Sun Dial would change throughout the year due to the precession of the Earth's axis, you can infer the length of night. However, once we realized that quartz is really good at defining a second, we were able to use oscillation as a means of telling time without sunlight.