Because Java can only use TCP/IP connections, the Postgres postmaster must be running with the -i flag.
Also, the pg_hba.conf file must be configured. It's located in the PGDATA directory. In a default installation, this file permits access only by UNIX domain sockets. For the JDBC driver to connect to the same localhost, you need to add something like:
host all 127.0.0.1 255.255.255.255 password
Here access to all databases are possible from the local machine with JDBC.
The JDBC Driver supports trust, ident, password and crypt authentication methods.
Read the upstream documentation. For corrections, first check the current manual.