Night Time Lighting

How do I do this? I want a black sky with gray fog and everything to appear slightly lit.

what have you tried? Are you using BP sky? Have you added a fog?

SkySphere, Directional Lighting, Atmospheric fog

and what does it look like? Have you made it look like night at all?

I can tell you how I achieved my Night Time Lighting, I was going for a moot lit night with clear skies.
I created a custom texture and material and applied it to the sky mesh that comes in the engine, I made the material in Maya using a spherical bake and constructed from textures I made in Photoshop. The moon was created by making a mask in Photoshop, and using it to create a billboard sprite and using a BlackBody node in the material to get a nearly correct color temperature, the sprite is in screen space scale so it’s always the same size in the sky.
Lighting consists mainly of 2 lights, a directional light with an intensity of .25 and a kind of cool warm blue gray color, and there is a sky light to fill in the shadows a bit more. The lovely effect of an atmosphere comes from an Atmospheric Fog.