When you go to start a new mission, the game changes weather and time of day. It should be fairly obvious if it is day or night, but there is a symbol in the top-right showing the time of day if the weather is clear (sun or moon icon).
Day and night are chosen by what time it is for you - day is 6am-6pm and night is 6pm-6am.
If you can't wait, you can change the time of day by altering your clock. Simplest way is to change the time zone by closing the game, right-clicking your computer's clock and Adjust date/time, and set your time zone earlier or later, and opening your game again.
Simply complete five missions in the day to unlock this!