I would do this:
1. Download the files from your wordpress install to your computer.
2. Export your database and download to your computer.
3. Upload the wordpress files to your subdomain using FTP (etc.)
4. Create a new database for your new install & import the databse.
5. Setup the wp-config.php file to point to the new database etc.
That should be all you have to do for the most part the ease of doing it depends on your hosting setup etc. If you have phpMyAdmin then the exporting/importing can be easy after you have made changes.
Tip when updating live site...make your life easy and DO NOT OVER WRITE THE wp-config.php FILE when uploading any changes.
Hope this information helps. :-)
There are also some good tips on this page too: http://codex.wordpress.org/Moving_WordPress