Using the Menus...

Open a cloud notebook

Choose File Open from Wolfram Cloud... and open the cloud notebook you want to copy to the desktop. Although the cloud notebook appears on the desktop, it still resides in the cloud:

Save the notebook on the desktop

Use File Save As to save a copy of the cloud notebook on the desktop:

Programmatically...

Open a cloud notebook

Open the cloud notebook you want to copy to the desktop. Although the cloud notebook appears on the desktop, it still resides in the cloud:

Save the notebook on the desktop

Save a local copy of the notebook:

In[2]:=
Click for copyable input

Using the Download Menu Item...

Download a notebook to the desktop

Choose File Download. Depending on your browser, either the notebook will be automatically downloaded to the desktop or you will be asked what you want to do with the notebook:

Open the downloaded notebook on the desktop

Choose File Open on the desktop and open the downloaded notebook: