See also Browser.StartDownload().
In CEF 3 downloads are handled automatically if ApplicationSettings.downloads_enabled is set to True (default). A default SaveAs file dialog provided by OS is displayed. If the download is aborted by user LoadHandler.OnLoadError will get called with errorCode ERR_ABORTED.
There is no download progress available. If you need such feature you will have to create a custom implementation of downloads. It would need to be investigated which callbacks from client handlers would allow for such implementation. Take a look at RequestHandler.OnBeforeBrowse, OnBeforeResourceLoad, and/or ResourceHandler.
On Linux there is a bug and ERR_ABORTED is reported even for successful downloads. See the comments in the wxpython.py example.
A download handler with callbacks like OnBeforeDownload and
OnDownloadUpdated may be exposed to CEF Python in the future.