In a cloud-computing environment we pay for the services that we use. So main criteria to measure a cloud based service its usage.
For computing resource we measure by usage in terms of time and the power of computing resource.
For a storage resource we measure by usage in terms of bytes (giga bytes) and bandwidth used in data transfer.
Another important aspect of measuring a cloud service is its availability. A cloud provider has to specify the service level agreement (SLA) for the time for which service will be available in cloud.