Multiply Layers tend to darken and add chroma in a very dull application. This is great for slowly building up colors and adding texture and tone to your image. It is very much like working with traditional watercolor. Great for building shadows and toning your image.
Screen layers are essentially the opposite of multiply, these also add color slowly, but they lighten instead of darken. I use these to add direct lighting over the dark layers below. By picking a warm yellow color here I am able to slowly work up a nice natural looking lighting effect to my figure.
Soft Light Layers are bonkers. They have no master, and obey no man. The math that governs them is not fully known to science. What I do know is that when a bright color is used on a soft light layer, it will allow for a very bright saturation of color which does not affect the details beneath it. For instance, I used a bright green color on a soft light layer to really pop the bright greens out from the rest of the image.
Color Dodge Layers scorch out highlights. They are extremely brutal and should be used VERY sparingly. Too much and you are lighting your birthday cake candles with a flamethrower. But when used sparingly, they can help to intensify your brightly lit areas as well as any glints of detail light. I use Color Dodge layers to sharpen highlight areas, add rimlights, and sharpen object profiles against their backgrounds. When alternated with multiply layers it will help push the value range of the image.
Color Layers. Not shown here because I use them so sparingly, but I do use basic color layers to push and pull color in limited areas. The Color layer mode is the classic means of photo-tinting, (and I need not badger you any further with warnings there). Just know that you shouldn't overuse them, but that in limited doses they are excellent. For instance, killing chroma: If an area is too red, I can select a blue color and lightly apply it on a Color Layer and it will pull the red back into check.
Normal Layers. Finally, there is just no escaping at least some opaque work for me when I work like this. But now that we have already established our value range and our colors are fully laid out, we can add details and opaque work that blends rather seamlessly with the rest of our image. I also use it very transparently and often set the layer opacity to less than 50%.
This general sequence offers me solutions to the problems I generally face as I work through an image. Everyone's artistic temperament is a little different, so play around with the different modes in different sequences and see what works best for you.