This method is for a default WordPress archive taken from WordPress.org site, without external plugin. The explaination are against WordPress 3.8.3, upgrading from version 3.8. We will assume here, that your public web directory is www/, but it depends on hosting service, distribution or your own configuration.
Before starting the update, SAVE YOUR FILES AND DATABASE. I also assume that you use the default wordpress directory for serving your blog and database named wordpress.
tar cf wordpress.tar www/wordpress; gzip -9 wordpress.tar # Archive directory containing WordPress installation.
mysqldump -a wordpress >wordpress.dump; gzip -9 wordpress.dump # Dump the associated mysql database