How to create user for a db in postgresql?

I have installed PostgreSQL 8.4 on my CentOS server and connected to root user from shell and accessing the PostgreSQL shell.

I created the database and user in PostgreSQL.

While trying to connect from my PHP script it shows me authentication failed.

How do I create a new user and how to grant permissions to them for a particular DB?

From CLI:

$ su - postgres 
$ psql template1
template1=# CREATE USER tester WITH PASSWORD 'test_password';
template1=# GRANT ALL PRIVILEGES ON DATABASE "test_database" to tester;
template1=# \q

PHP (as tested on localhost, it works as expected):

  $connString = 'port=5432 dbname=test_database user=tester password=test_password';
  $connHandler = pg_connect($connString);
  echo 'Connected to '.pg_dbname($connHandler);

Create the user with a password :

http://www.postgresql.org/docs/current/static/sql-createuser.html

CREATE USER name [ [ WITH ] option [ ... ] ]

where option can be:

      SUPERUSER | NOSUPERUSER
    | CREATEDB | NOCREATEDB
    | CREATEROLE | NOCREATEROLE
    | CREATEUSER | NOCREATEUSER
    | INHERIT | NOINHERIT
    | LOGIN | NOLOGIN
    | REPLICATION | NOREPLICATION
    | CONNECTION LIMIT connlimit
    | [ ENCRYPTED | UNENCRYPTED ] PASSWORD 'password'
    | VALID UNTIL 'timestamp'
    | IN ROLE role_name [, ...]
    | IN GROUP role_name [, ...]
    | ROLE role_name [, ...]
    | ADMIN role_name [, ...]
    | USER role_name [, ...]
    | SYSID uid

Then grant the user rights on a specific database :

http://www.postgresql.org/docs/current/static/sql-grant.html

Example :

grant all privileges on database db_name to someuser;