Copy/Paste should work like this...
Select a component, or drag-select a group of components.
Click copy on the Geom Browser
Click to select the component that you want the pasted components to be a child of -- select none to paste as a top-level component.
Click paste in the Grom Browser
You should get a new duplicate component -- it will lie exactly on top of the first one, so you might not see it.
You can use ^C ^V shortcuts -- but the mouse context must not be in a text (or number) entry box -- then, your OS will try to copy/paste the text.
If you're seeing different behavior, please try to explain what you're seeing in very specific detail so we can replicate your steps.
Rob