From your Zola Weddings dashboard, find where it says "Visible to Guests?" and switch the red toggle to "Yes." Congrats, your website is public!
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. And if any of your pages are a work in progress (or you don't want to feature them at all), you can always change any page's visibility to "Hidden."
You can control if you want your website to show up in Google searches from your Account page, within the Wedding Details - Privacy section.
Read more about search engine (ex] Google) settings here.