The only way this layer can interact with layer below it is by using the opacity slider. Instead of always using the opacity slider to change the transparency of the layer, use the number keys on your keyboard. This will create a dissolving effect, hence the name. If you look at the image to the left, you'll see that certain pixels were chosen, and others weren't, it's like that throughout the entire layer. So far all the blending modes speak for themselves, that's also true for the Multiply mode.
Screen mode is used for highlighting, and making the layer appear lighter.
Since highlights cannot be shown with black, no effect will appear by applying the Screen mode to an entirely black layer, or part of a layer. Another way to look at highlights is if you were to shine a light on something, it would look lighter to you than it actually is, the same principle applies for the Screen blending mode. Overlay mode will change the contrast and opacity of the layer to varying degrees depending on the lightness and darkness of that layer. Overlay is often used for digital painting, where artists will sketch out their landscapes and characters, then scan them in, and use Overlay mode to view there art while painting behind it. For Soft Light and Hard Light certain grays will appear completely transparent for some odd reason.