Modern society essentially denies night. When it gets dark outside, we turn on the lights and keep going. Then we snooze well past sunup, at least in the summer. (The extreme version of this is the Las Vegas casinos, which do not have windows or clocks, so that you'll have no idea how long you've been there.) The Middle Ages did not have this option.
When artificial light was provided by wood fires and candles, both expensive and neither very bright, people made the most of real daylight. As soon as dawn began driving back the shadows, when the rooster first crowed, well before the sun came up, people were stirring, getting dressed, going to Mass, getting ready for the day's activities. This was true of aristocrats and peasants alike. Sunup was considered the first hour of the day, called Prime (click here for more on telling time then).
At the other end of the day, as the sun went down people started thinking of turning in. They might have a last snack ("supper") and then went to bed. This meant that, for half the year, they were (potentially) in bed for 10-12 hours a night, much more in midwinter. (Click here for more on medieval beds.)
In practice they would not sleep this whole time, even though, as most of have noticed, the hibernation reflex becomes powerful when it is very cold and dark outside. And snuggled into bed with at least one other person is the warmest way to spend a cold night. Often they would wake in the middle of the night, maybe just stay cozy in bed and have a nice conversation, or maybe get up and do a few simple chores. Monks would rise for the night offices, prayers and singing of the psalms. Any such rising required candles and so was carried out with minimal light. After an hour or so, they returned to sleep.
In the summer medieval people had the opposite problem, especially in northern Europe--the nights would be very short, much too short to get a full night's rest. As a result, it was normal to take a nap in the afternoon.
A similar pattern has been observed in some rural villages in Africa, where most of the population will go to bed at sunset. Some however stay up to watch for predators, and during the night others may rise and take a turn, while the first watchers retire. Songs and stories around the fire help the hours pass.
What did medieval people wear at night? Nothing at all. We now take pajamas for granted (or nightgowns, or a T-shirt with boxers). But clothing was too valuable to have an extra set just for sleeping. Monks slept in their robes (probably needed for warmth, because it was one person per bed, and any self-respecting austere house had inadequate blankets), but everyone else slept naked.
Pajamas (or pyjamas), by the way, really only came into regular use in the nineteenth century. The word comes from India, via the British Empire, and originally meant a loose pair of trousers with a drawstring waist. The British in India found them great for lounging and then for sleeping.
In the early modern period (sixteenth through eighteenth centuries), it became for the first time fashionable to stay up after the sun went down. This is when plays and operas began to be put on in the evenings. Staying up late, because one could sleep late in the morning, was a sign of wealth and luxury, as was being able to afford all the candles that made it possible.