First thing first, go to the Settings > Build triggers section of your administrative area and select the trigger where you want to integrate Site Search with (ie. Production). Enable Site search and specify your Website frontend URL. That's the address from which crawling will begin. To start the first indexing of content, press the Publish changes button.
If you go to the Settings > Activity log, you will see that after the website gets published, DatoCMS will start spidering your website. When spidering ends (it may take a while, depending on the size of your website), you'll see a Site spidering completed with success event in your log. Clicking on the Show details link will present you the complete list of spidered pages.