There are numerous ways to accomplish this. This is not in-depth but should point you in the right direction:
1. Backup the MySQL database using phpMyAdmin.
2. Using an FTP program such as FileZilla and download the entire theme folder.
3. Install a fresh copy of WP into a new folder. Be VERY sure not to install into the root folder. If your host has a one click installer that allows you to change the installation folder that will make things easier but again, be careful of where it is being installed.
4. Import your database backup into your new empty database using phpMyAdmin.
5. Upload the theme folder to
6. Edit wp-config and add:
http://example.com/example to the actual domain name and folder.
This needs to be done because the the database restore is going to have your WP site URL and home URL configured for the live site.