What you may want to look for is the opacity setting on the particular layer you are working on. It’s a tiny tiny dial on the “Layers” window, that you can drag back and forth to make the image more or less opaque.
I am very familiar with changing the layer opacity. The issue arises when saving the image - how do I save it as a png? Any other type of saving will insert the white (except psd, of course. But jpeg, gif… I need to be able to use it in other programs, not just photoshop, so it has to be usable and readable by other programs.)