If the authentication email has not arrived, work through these four steps in order. The first three solve it most of the time, and the fourth always will.
The authenticate screen shows the email address you entered when you signed up. Read it carefully, because a single typo is the most common cause.
If it is wrong, the address cannot be corrected from that screen. You will need to sign up again with the right one. See How do I sign up as a volunteer on Vome?
Mail providers often file messages from a sender they do not recognise straight into Junk or Spam.
If you find it there, move it into your inbox rather than just opening it. That teaches your provider to trust Vome, so the next email, such as a shift reminder or an approval notice, arrives where you expect it.
On the authenticate screen, click resend authentication email. Give it a couple of minutes before assuming it has failed again.
If none of the above works, submit a ticket. You can also email support@vomevolunteer.zohodesk.com.
Either way, use the same email address you signed up with. That is what lets the team confirm the address is yours, and they can then bypass the authentication step for you.

That is a different problem with different causes. See Why can't I log in to my account?