Upload the unapi folder containing all source files to your plug-ins folder, usually wp-content/plugins/
Login as an administrator and activate the plug-in via the Plugins menu
Choose an identifier prefix -- an arbitrary string, preferably URI-valid -- and enter it via the unAPI submenu of the Options menu. Or, alternatively, use the default value - no fuss, no muss.
Voila! All of the posts in your WordPress blog are now published via unAPI.