Adding a subdomain or domain alias in a VPS is very similar to adding a domain.
To add a subdomain to your VPS you need to add the virtual host section in Apache's configuration. You will also need to add the subdomain DNS record (with a CNAME record) in your domain DNS configuration.
The same applies to a domain alias.
Let us know if you need help with any of these steps and we will gladly help you set it up.