1.3.2 is really old. If it is an application with a lot of custom stuff then there may be some pain. Upgrading Xataface is really just a matter of just replacing the "xataface" directory. The index.php file for your application will include a line line this:
require_once 'path/to/xataface/public-api.php';
df_init(__FILE__, 'path/to/xataface')->display();
Or something like that. There will at least be a "require_once" for the xataface public API, and there will be a call to df_init().
Just download the new xataface somewhere. Probably in the same directory as your current xataface. E.g. path/to/xataface-new. Then update the index.php file
require_once 'path/to/xataface-new/public-api.php'
and
df_init(__FILE__, 'path/to/xataface-new')....
When you toggle versions like this you'll also need to clear out your templates_c directory so that the templates don't conflict.
If it doesn't *just work*, then post the issues you are having, and there might be some config options that can be set to smooth the landing. Your error log will provide clues, so make sure to watch that if things aren't working.