Selecting Layer → New Layer in the image menu. This brings up a dialog that allows you to set the basic properties of the new layer; see the New Layer dialog section for help with it.

Selecting Layer → Duplicate Layer in the image menu. This creates a new layer, that is a perfect copy of the currently active layer, just above the active layer.

When you "cut" or "copy" something, and then paste it using Ctrl+V or Edit → Paste, the result is a "floating selection", which is a sort of temporary layer. Before you can do anything else, you either have to anchor the floating selection to an existing layer, or convert it into a normal layer. If you do the latter, the new layer will be sized just large enough to contain the pasted material.