How my site looking like this in google

[ozzy47]

Well it would be like this.

<script type="application/ld+json">
{
   "@context": "http://schema.org",
   "@type": "WebSite",
   "url": "http://YOURSITE.com",
   "potentialAction": {
     "@type": "SearchAction",
     "target": "http://YOURSITE.com/search.php?do=process&q={search_term_string}",
     "query-input": "required name=search_term_string"
   }
}
</script>

Replacing YOURSITE.com with your actual site. Add the code to the end headerinclude template.

Will this work? I dunno, only time will tell.
How long will it take? I do not know that either.

But you can see it is working by going to http://YOURSITE.com/search.php?do=process&q=searchword

Replacing YOURSITE.com with your actual site and searchword with a actual search keyword.