uuu thank u anon!! i hope this can explain it :^o
i use overlay all the time to make colours more vibrant and to make areas warmer or cooler. good for colourful ambient light (like glowy magic stuff).
multiply is really good for establishing a light source very quickly!! play around with the hue to get shadows with cool colours. for more detailed work you can use two or three tones on a multiply layer for more dimension.
screen is something i only recently started using regularly! it’s really great if you have a very bright light source. you can also use screen and paint on the edges of a backlit character to make the lighting more intense. a good thing to know about screen layers is that the darker the colour you use, the less it lightens; using black on a screen layer leaves no effect on the colours underneath (the opposite is true for multiply layers!).
and you can also use these layers for an entire painting instead of just on a character! i don’t have a visual example on hand, but stuff like making the area around a warm light source warmer, making a light source brighter and more vibrant, or using gradients set on multiply or screen are just some of the ways you can apply these to a full painting :)