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;