site search with in the site.

I think that you are best off using a JSON datafile and JavaScript to handle the logic.

Have a look at https://youtu.be/1iysNUrI3lw

You will need a local web server like WAMP or similar if you want to test the site locally. This is because the Fetch API is used in the example.

You can make it easier for yourself by using a few Dreamweaver extensions

1. App Connect

2, App Connect JSON Data Source

3. App Connect Data Traversal

Or use Wappler which includes the extensions.

If you don't want to use Google's custom search feature (there are pros & cons with it), look at FREEFIND.com which has both free version with ads and paid version without ads.  After Freefind indexes your site's content (usually within a few hours), you can activate the search form with some copied & pasted code.

Post back if you need more help.

Probably the easiest way would be to add a Google search to your site: https://support.google.com/programmable-search/answer/4513751?hl=en&ref_topic=4513742 

There's nothing in DW that can do this for you though. DW has a couple of templates with a search bar, but it's just an html form. It doesn't do anything until it's attached to some server scripting. If you want to add true search functionality to your site that isn't controlled by Google's crawlers, you'd need to create a database driven site, then use a server side scripting language, like PHP, to search the database when a view submits the form (search bar) and display results.