The first sentence is that there is no single regex that perfectly validates every technically valid email address. I think that is a good start.
It then recommends the regex used for <input type="email"> and explains that this would cover the majority of email addresses used by actual people. It also shows an improved regex that handles dot-atom local parts, quoted strings, domain names, and IPv4 domain literals, but doesn't cover things such as comments, full IPv6 literals, or internationalized addresses.
It ends with the only correct advice (in my optionion): Send a confirmation email.