How to make animated fog?

Hello! I am making a survival game with camera angle like in "Don't starve!" and I was thinking about some background effects. In this exact case I am thinking about animated fog, fireflies for example etc. The problem is that I don't really know how to make such effects. Some examples are the backgrounds of the games "Pinstripe" and "Once upon a coma". I will try to paraphrase if needed. I want to make for example fog, rain, fireflies etc. Probably something like overlays are used but I am not sure. Thank you to everyone who helps!

 

In this template I used a particle system with some cloud-like particles moving very slowly. The camera angle is at around 45 degrees and the fog is created between the camera and the 2D ground+characters.

 

Interesting. Thank you a lot! I will definitely look deeper into that.