Setting up a new DataStax Enterprise cluster on Amazon's cloud can be done in about ten minutes using DataStax OpsCenter. First, install DataStax OpsCenter Enterprise on an existing EC2 machine and ensure its interface parameter is configured properly in the config file. Next, use OpsCenter's Create Cluster option to create a new database cluster with desired specifications such as number of nodes and software components like Cassandra, Hadoop, and Solr. Finally, click the Build Cluster button, which will automatically set up the cluster. The actual time for this process may vary depending on factors such as instance spin-up time and download speed.