It's as simple as calling the webservice using whatever method you need (REST, SOAP, etc.). For .NET developers using .asmx or WCF SOAP services, just generate the proxy like you normally would. In this model, there is no difference between what you do onpremises when the cloud is the client.
You would look at using the ServiceBus when you are hosting your own services (as opposed to consuming them), typically behind firewalls onpremises, and you want to give secure access to them or integrate them into cloud scenarios. There are other scenarios and capabilities of course, but that is a main one. If you simply want to consume another web service, the ServiceBus has nothing to do with that.
As long as the 3rd-party web service endpoint is reachable, use it the same way you'd use it from an on-premises server. If you need to connect to a service endpoint behind someone's firewall, then you'd want to consider AppFabric Service Bus.
Just remember that you'll be paying for bandwidth out of the data center (unless the 3rd-party web service is Windows Azure homed, and in the same data center).
