Site search is being rolled out to New Sites so the text below is redundant -->

There is no search feature in New Sites yet. Google has announced that Site Search will be added when New Sites are rolled out. See Deprecation Timeline

One way to add a search engine ahead of the eventual roll out is to use FreeFind

After you create an account and tell it to index your site you can add a link to the site search as I have done at the top of this page. On the HTML page scroll down to 'Text links -- links to your search engine pages ' and copy one of the links to embed in your page. You can also insert a search bar. See below.

There will be advertisements on the search results. They can be removed by subscribing. Subscriptions start at $5/month.