How to create a sub-domain on a website?

You don't have to buy a separate domain name to create subdomains. Basically, all you're doing is create a new DNS record.

For example, if you want to create a sub.domain.com and you want to point it to a specific IP, you'll be creating a A record like this:

sub IN A 12.34.567.89

If you want to create a subdomain and point it to another website, you'll be creating a CNAME record, like this:

sub IN CNAME www.anotherdomain.com

It depends on who is hosting your website and who is hosting your domain name.
What you need to do is to add a CNAME record in your DNS setup, pointing to the host name/ip address of the server that will be hosting the subdomain (this varies based on who provides your domain name). Then you need to configure your web host to respond to requests to that subdomain.
To give you a definitive answer, we need to know who you are hosting your website and domain name with.