It its popular to reference a PostgreSQL database with credentials via a URI, but neither psq --help nor man psql (v9.3.4) indicate how to do it.

@yann_ck showed me you can pass it as the first argument:

$ psql postgres://USERNAME:PASSWORD@babar.elephantsql.com:5432/jszlmeae
psql (9.3.4, server 9.2.8)  
SSL connection (cipher: DHE-RSA-AES256-SHA, bits: 256)  
Type "help" for help.

jszlmeae=>