You didn't mention where is your domain located, at the registrar or if it was registered from the WordPress.com and Blogger.com's panel. That should change the instructions set completely. So I am covering all the possible scenarios for you.
Domain registered at registrar: Here registrar means service like godaddy, namecheap and others. If you have domain registered in site other than the WordPress.com and blogger.com. Then in such case you have to create the subdomain from the registrar control panel itself. So the instruction for that would vary from company to company. And no two companies have same dashboard so it's hard to generalize steps. In case of godaddy however you get to manage the domains from the domain > settings > subdomain. As for namecheap, go to domain > subdomains.
Domain registered at WordPress.com : In case if you have purchased the domain from WordPress.com then the mapping for the subdomain will be as follows.
1. Add CNAME record : This can be done by going into your WordPress.com dashboard. You can find specific instructions here : https://en.support.wordpress.com/domains/custom-dns/
2. Add domain mapping: After CNAME, you have to create and add the subdomain into your WP records. This can be done by following instructions here : https://en.support.wordpress.com/map-existing-domain/
After completing these two steps, you'd be able to use the subdomain for your Wordpress.com blog the way you want. You can set redirects or you can use the new blog on it. Or you can also use the current site on that blog.
Domain registered at cPanel host with WordPress installation If your wordpress blog is hosted on some cpanel host. Then the wordpress.com instructions do not apply to you. In such case you have to go to cpanel add the subdomain by going to yourdomain.com/cpanel. Login to the Domains section and add the subdomain. You can then make redirects or install new or move existing wordpress.com setup over there.
Domain registered at another registered to be used on blogger: In this case all you have to do is go to your registrar. And create new subdomain. And then point the subdomain to "ghs.google.com". You may also have to update cname records too. This change takes place in few hours or even a day or so.
Domain registered at blogger.com: In this case you have to open your blogger.com custom domain app central page. You can access that from : http://google.com/a/cpanel/domain.com". Note that here domain.com means your domain name. After you login to the dashboard go to Domain Settings > Domain Names > Domain advanced settings. Here you can add the subdomain and point to the respective CNAME records. This way you can map the existing blogger.com blog to subdomain or even other domain redirection.
If you think you can't do these changes on your own, then you can also ask the support department of blogger.com and wordpress.com to help you on this.