You can find the name servers you need to use in your welcome email or HostGator control panel. For more information, please see this page 

In order to point the domain to your server, please login here to manage your domain's settings

You're seeing this page because your domain is setup with the default name servers: ns1.hostgator.com and ns2.hostgator.com 

How can I avoid this in the future?

When you purchase domain names from register.hostgator.com, check the box next to: "Set Custom Nameservers (Optional)" in the domains cart and add your desired name servers. The domain will be registered with the name servers configured from the start

Our knowledge base has a lot of resources to help you!
• How do I change my name servers?
• When will my domain start working? (Propagation)
• Can I use my account and my site even though my domain name hasn't propagated yet?
• What is an addon domain?
• How do I create/remove an addon domain?
• What are private name servers