Twilight or the "Blue Hour"

Twilight hour helps balance the lighted signs of the Dairy Queen

Wikipedia defines it:  

Twilight is the time between dawn and sunrise or between sunset and dusk, during which sunlight scattering in the upper atmosphere illuminates the lower atmosphere, and the surface of the earth is neither completely lit nor completely dark. The sun itself is not directly visible because it is below the horizon. Owing to the distinctive quality of the ambient light at this time, twilight has long been popular with photographers and painters, who refer to it as the "blue hour", after the French expression l'heure bleue. Twilight is technically defined as the period between sunset and sunrise during which there is natural light provided by the upper atmosphere, which receives direct sunlight and scatters part of it towards the earth's surface.

The sky is not black and give a great dark blue at this time of day.

If you know the time that is for sunrise or sunset then you need to be about 20 minutes from that time.  For sunrise minimum of 20 minutes before it and sunset 20 minutes afterwards.

My suggestion for sunrise is to get there one and half hours before sunrise and for sunset be ready about 30 minutes before sunset and plan for up to an hour after sunset.  Depending where you are in the world, due to the angle of the earth to the sun you might have a long time or a very short time to shoot this magical hour.

Cloud patterns are still visible.  Sometimes you get the sun still catching the clouds.