psql postgres
\l
\q
psql postgres
CREATE DATABASE testdb;
\q
You can the reconnect as the new database...
psql testdb
or simply switch to it before logging out...
\c testdb
CREATE DATABASE testdb ENCODING 'utf-8';
Runs from the command line rather than psql (or other client)
DROP DATABASE IF EXISTS name
If you list databases in a fresh instance you will see three databases:
postgres
template0
template1
By default, a new database will be created by cloning template1.