To backup a liveSite installation, you will need to make a copy of the liveSite file structure, and also a copy of the liveSite database.
1) Export your MySQL database to a file via PHPMyAdmin or by running this command if you have access to the command line:
[/path/to/mysql/bin/] mysqldump -u [username] -p [database_name] > livesitebackup-todaysdate.sql
You will find the database_name, username, and passsword in the liveSite config.php file.
2) Download the .sql file to your computer and place it in your backup folder.
3) Backup all of the liveSite directories and files from the web server:
/livesite (including everything inside this directory)
This assumes that liveSite is installed in the livesite folder off of the web root.
NOTE: Daily backups are included with all cloud hosting plans.