How to add a subdomain

A subdomain like blog.example.com or app.example.com is just another DNS record on your existing zone:

1. Decide where the subdomain should point — an IP address or another hostname.
2. In DNS, add a record with the host set to the subdomain label (blog, app, shop — you don't type the full domain, just the left-most part).
3. Use an A/AAAA record if you have an IP, or a CNAME if you're pointing at another hostname (e.g. a SaaS provider's something.provider.com).
4. Save and wait for the TTL.

To hand an entire subdomain to a different DNS provider, instead add NS records for the label pointing at their nameservers — this delegates that branch of your zone to them. For most cases a simple A or CNAME is all you need.