When I try to connect it via PHP or PostgreSQL using following syntax:

psql -d myDb -U username -W

It gives me an error that read as follows:

psql: FATAL: Ident authentication failed for user "username"

How do I fix this error?

To fix this error open PostgreSQL client authentication configuration file /var/lib/pgsql/data/pg_hba.conf :

# vi /var/lib/pgsql/data/pg_hba.conf

This file controls:

1. Which hosts are allowed to connect
2. How clients are authenticated
3. Which PostgreSQL user names they can use
4. Which databases they can access

By default Postgresql uses IDENT-based authentication. All you have to
do is allow username and password based authentication for your network
or webserver. IDENT will never allow you to login via -U and -W
options. Append following to allow login via localhost only:

local all all trust
host all 127.0.0.1/32 trust

Save and close the file. Restart Postgresql server:
# service postgresql restart

Now, you should able to login using following command:
$ psql -d myDb -U username -W