In order to create a databases, the PostgreSQL server must be up and running (see Section 16.3).
CREATE DATABASE name;
where name follows the usual rules for SQL identifiers. The current user automatically becomes the owner of the new database. It is the privilege of the owner of a database to remove it later on (which also removes all the objects in it, even if they have a different owner).
The creation of databases is a restricted operation. See Section 17.2 for how to grant permission.
Since you need to be connected to the database server in order to execute the CREATE DATABASE command, the question remains how the first database at any given site can be created. The first database is always created by the initdb command when the data storage area is initialized. (See Section 16.2.) This database is called template1. So to create the first "real" database you can connect to template1.
The name template1 is no accident: When a new database is created, the template database is essentially cloned. This means that any changes you make in template1 are propagated to all subsequently created databases. This implies that you should not use the template database for real work, but when used judiciously this feature can be convenient. More details appear in Section 18.3.
createdb does no magic. It connects to the template1 database and issues the CREATE DATABASE command, exactly as described above. The reference page on createdb contains the invocation details. Note that createdb without any arguments will create a database with the current user name, which may or may not be what you want.
Note: Chapter 19 contains information about how to restrict who can connect to a given database.
Sometimes you want to create a database for someone else. That user should become the owner of the new database, so he can configure and manage it himself. To achieve that, use one of the following commands:
CREATE DATABASE dbname OWNER username;
from the SQL environment, or
createdb -O username dbname
You must be a superuser to be allowed to create a database for someone else.