How do i set up a new domain

If you don't already own a domain (like 'something.com') there are a lot of services which offer them and provide email and other facilities. Basic domains are not particularly expensive, though if you want one rusing your own name you are unlinkely to get it by now unless you do something adding a number to it as many surnames have already been used to create domains (mine included).

Domain names usually have to be re-subscibed to every two years, though some services offer longer subscriptions and arrange the renewals themselves.

When buying a domain you should check that the provider can mask your address in 'whois' results otherwise your personal address will be available for the world to see. Some will charge for this.

Once you've obtained a domain and an email address such as you@yoursurname.com you can proceed with Apple's facility.

You could look at https://getdotted.com/ . I wouldn't have thought you'd get a free year anywhere, though you never know but you'd be told what the cost is. The usual domains like .com, .co.uk and so on aren't usually expensive. The more exotic ones belong to other coutries and there can be restrictions on them, and they can be more expensive.

Use Custom Email Domain with iCloud Mail - Apple Support