You have to authorize your new user to connect to database by editing your pg_hba.conf file (often located on /etc/postgresql/9.4/main/pg_hba.conf with 9.4 being your installed version of PostgreSQL).
Do to so, add a line on it like this one :
# TYPE DATABASE USER ADDRESS METHOD
local django django trust
Supposing that you created a database name django for your django user.
It only allow your user to connect locally, if you want to allows him to connect via TCP/IP, line is more like
# TYPE DATABASE USER ADDRESS METHOD
host django django 192.168.12.10/32 md5
Where 192.168.12.10 is the IP from where your django user will reach your database.
Read comments on pg_hba.conf file, they explain pretty well how it works. Or have a look at this documentation on PostgreSQL website.