The Client based approach is a lighter-weight yet more powerful API than JDBC.
The Client object should be connected to each of the servers in the cluster, or you can set the "TopologyChangeAware" property to true on the ClientConfig object prior to creating the Client object, then connect the client to any server in the cluster and it will create connections to all the others automatically.
The application will then interact with the database using this Client object, which has connections, rather than using a JDBC Connection object. Since the Client object is thread-safe and can support multiple simultaneous invocations of callProcedure() on multiple threads, there is no need to create a pool of Clients.
For more details on the Client interface, see Using VoltDB Chapter 6. Designing VoltDB Client Applications
Disclaimer: I work for VoltDB.