I can use Export to create files in the WolframClouduserFiles area. How do I bring these files to my local storage, either programmatically or by user gestures?
Can't you open the document then use "Save", the usual way?
As far as programmatically, Notebooks would be an avenue but I've never used "cloud save" with these myself - i assume it's pretty simple if your already familiar with Notebooks
(Clouds are just file servers (with some app level enhancement) with a fancy name; it's not the same definition as "telephone company cloud" people used to talk about.)