Their documentation says they can accept a JSON Post or an XML post request, which means you would have to generate these requests and send them from Magento.
I suggest looking into tutorials on creating API based shipment and payment extensions.
Here is a tutorial for an API based payment extension. You can adapt the sending/receiving principles to your shipment extension: http://www.excellencemagentoblog.com/magento-create-custom-payment-method-api-based