Everything is done with HTTP requests (duh), if you want to upload a file then you make an HTTP POST request with the file data (just like with a normal file upload form) and the associated meta-data. The servers then process the file and give you links back to access it.

Fetching files will be processed similar to a download, php will "fetch" the file and then write it to disk. Then php can move or rename it via its functions.

Renaming, copying, and deleting files are all done with a single http request with a relevant response code (pass, fail, more info needed...).

Really, it's pretty simple and the included libraries seem to cover everything that most apps will need.