Basicly you buy the domain that you like. Cloudflare sells them at cost. Porkbun has a huge verierty to choose from. After you buy the domain you will have a control panel where you can configure “where” the domain points to.

After you find an email provider that supports custom domains and sign up they will provide you with where to point the MX (email part of the domain) record. Typically some site they control.

In the control panel you point your domain MX records at the address they provide and you can start receiving email at the email of your choice.

After you confirm you can receive email you should then add stuff to your dns control panel like DKIM and SPF so your email won’t be marked as spam. The email provider will give you specific strings to copy paste.

If the email provider starts misbehaving or you just want to switch it’s just a matter of signing up somewhere else and re pointing the domain MX records while you keep the same email. It’s a little more complicated but I means you truly own your email. That and it will typically cost a little bit of money.