To install Backup Pro you follow the same steps as any other ExpressionEngine add-on:
You'll also have to make sure that the directory "backups" and all it's contents are writable by the webserver but Backup Pro will let you know if it's not.
Because Backup Pro stores sensitive information in the form of FTP and Amazon S3 credentials an encryption key within ExpressionEngine needs to be set. If your installation doesn't already have one set all you have to do is open up your config.php file and paste the below variable inside:
$config['encryption_key'] = "YOUR KEY SHOULD BE LONG AND RANDOM";
See the Codeigniter documentation for details.
Backup Pro also requires that PHP have the Zip library available for the Database Restore process to work.