By implementing Website and Search Action markup, your content can be made eligible for Google's Sitelinks Search Box feature. 

How to create Sitelinks Search Box markup

Step 1: Create a Website data item

• Fill out the name and URL properties for the Website data item (the name should match the name of the Website)
• use the potentialAction property to create a SearchAction data item

Step 2: Create a SearchAction data item

• Fill out the name property on the SearchAction data item (the name can be anything, but should be easily identifiable in a list of data items)

Step 3: Find the URL template

• The URL template is the base URL used for searching across your website. To find it:
  1. Search for any term on the site, in this case we're searching for "FAQ" on Schemaapp.com
  
  2. Copy the base URL before the term, in this case we're copying "https://www.schemaapp.com/?s=" but leaving out the "FAQ" because that will be replaced by a variable.
  
  
  3. Append the URL with a variable that will be replaced with whatever search term a user may enter. Wrap the variable in curly brackets. For example, {search_term_string}.
  
  4. Paste the base URL + variable in the target property of the SearchAction. In our example, the full value for "target" is "https://www.schemaapp.com/?s={search_term_string}"

Note: You only need to paste text into the target property. Google will automatically transform this value into an EntryPoint data item.

Step 4: Provide the query-input

• The SearchAction's query-input value must match the variable you provided for the target without the curly brackets and in this format: "required name=target_value". In our example that would be "required name=search_term_string".

Note: You only need to paste text into the query-input property. Google will automatically transform this value into a PropertyValueSpecification data item.

• Leave the "query" property blank. Google will fill this out based on the rest of the schema you have provided.
  
  

Step 5: Check your work

• Validate your structured data using the Schema Validator and/or Rich Results test and make any necessary adjustments. To verify the work that you’ve done, use the testing tools withing the Editor, or select "View JSON-LD", then copy the markup and input it as code into Google’s Rich Results Tool.

Here is an example of what the JSON-LD might look like:

<script type="application/ld+json">

{

    "@context": "http://schema.org",

    "@type": "WebSite",

    "potentialAction": {

        "@type": "SearchAction",

        "target": "https://www.example.com/search?q={search_term_string}",

        "name": "Search Example Site",

        "query-input": "required name=search_term_string",

        "@id": "https://www.example.com/#SearchAction"

    },

    "url": "https://www.example.com/",

    "name": "Example Website",

    "@id": "https://www.example.com/#WebSite"

}

</script>

Here is an example of what your search action data item will look like in the editor:

Note: If your site is on Wordpress, the Schema App plugin can automatically generate Sitelinks Search Box markup.