From your Zola Weddings dashboard, find where it says "Visible to Guests?" and switch the red toggle to "Yes." Congrats, your website is public!
When this is set to "No," no one can visit you website and it is private.
You can control if you want your website to show up in Google search or Zola search from your Website Mange Pages page, click Edit Settings.
Control search settings here.
Read more about search engine (ex] Google) settings here.
If you so choose, you can make your website password-protected by going to "Manage Website" in the Website section of your dashboard and selecting "Yes" on the "Password Protect" toggle. Read more about password protecting here.