First, be a good idea to do a full backup of what you have first ... the code directory, the data directory, and an sql dump of the db. Then ...
Edit the config.php file on live server changing the values you see old host and replace with new host.
Login as admin user to Moodle. There might be a link available for search and replace in the Site Admin menu. Search for 'replace'. If not available in 2.3, then go to: http://site/moodle/admin/tool/replace/
Search for http://oldsite/ replace with http://newsite/
'spirit of sharing', Ken