Hostgator will have given you DNS settings (Probably ns1.hostgator.com & ns2.hostgator.com).
You need to log into network solutions account and change the nameserver settings for your domain to the above settings
(They are probably set to ns1.networksolutions.com & ns2 or something similar, at the moment)
It will take 24-48 hours for the changes to become visible on the internet
