How to get Layer size (Width and Height)?

Option 1.

I have an action that does this:

Cmd+A, Cmd+C, Cmd+N

When I run this action I’m left with New document window. The width and height in the window are the clipboard image dimensions = your objects/layers dimensions.

You then can press Esc to close the window.

( On windows just think of the Cmd as Ctrl )

Option 2.

You can make a selection of the layer for example by ctrl or cmd clicking the layer thumbnail and then looking at the info panel F8, it will show you the dimensions of the selection.

From the upper right corner where you can see the arrow pointing down, you can find the options and within there you can set the ruler unit to pixels or what ever you want it to show.

Option 3.

Use Free transform Ctrl+T and when free transform is active, go check the Info panel F8 as shown above. This works even if the object is outside the document area.

Here’s another answer that is slightly related:
How to measure the distances in .psd

Especially the bottom part of the answer that lists methods to exporting layer styles as css, which includes width and height, of course.