Layers and layer groups
Make sure you can see the canvas of both the source and destination images.
On the source image, grab that layer or layer group and drag it over to the destination image.
As you're doing this, the whole destination canvas will sport a black border. This shows that you're about to drop in a layer (or layer group) into that image.
Release and you're done.
If you're doing this with a layer style, remember that the last selected layer of the destination is where the layer style will end up.
The above drag-and-drop method will not work with layer masks. They come with the entire layer or not at all.