There is an error in the Hostgator documentation for this.
If you are using Hostgator for DNS it automatically sets up the DNS completely for new subdomains when you use the create subdomain command in cpanel. You do not even have to use Hostgator as your registrar, as long as the name server entries at your registrar point to your Hostgator name servers, which are the name servers shown on the Hostgator cpanel screen.
The documentation error involves the Document Root field to be filled out when using the cpanel create subdomain command, which is needed when the subdomain files are hosted in the same hostgator account as the main domain. In the hostgator documentation, the example for the document root is "/public_html/blog1" as an example place to put the files for a new subdomain "blog1". This is incorrect- the document root you enter for the new subdomain in the cpanel subdomain command must NOT start with a SLASH. Remove the slash and use "public_html/blog1" (or wherever you want to put your files within public_html) and it just works.
Also, there is no delay for this, as long as your main site has already been set up. When you enter the create subdomain command correctly, it gets entered into the hostgator DNS at that time, and the internet already has the hostgator name servers as the authoritative name servers for your domain name. So you don't have to wait a few days or even a few hours. Sometimes you have to flush your browser cache.
Good luck, and more subdomains to you!