It depends on how north you are. If you are at the Arctic Circle, you get exactly one day where the sun doesn’t go down. During that day, at midnight the sun is at North and on the horizon. In the winter solstice, you get a day without the sun, as hiphiphopflipflapflop explained.
If you go far enough north to, say, 70 north, you get a few months of the sun not going down, during which it is at east during morning, south at noon, west in late afternoon/evening and north at midnight. Basically it goes in circles around you. Then after a few months of gradually shortening days, the sun sets in November:ish, comes up in February. Needless to say, the winters are very dark.
If you go south of the Arctic Circle, you have lots of light in summer and relatively dark winters, but you don’t actually get the midnight sun or a dark day.