For now, and though if can be done without, it's only explained how to install it using Composer.
Start by adding jadb/s3sync to your composer.json dependencies like so:
{
"require": {
"jadb/s3sync": "*"
}
}
Now update your dependencies:
php composer.phar update
Setting it up is just about copying and customizing a file:
cp vendor/amazonwebservices/aws-sdk-for-php/config-sample.inc.php aws.conf
vi aws.conf
To sync a directory relative/path/to/sync with the backups S3 bucket:
./vendor/jadb/s3sync/src/s3sync backups relative/path/to/sync dry verbose
The shell is based on JadB\S3Sync, check it out and build your own scripts.