Which results do you want to display on your website? Do need an improved search engine for an enhanced user experience? You're there!
WP-ISE: the Improved Search Engine for WordPress is a WordPress dedicated search engine, built with a single and simple goal in mind: offer a better search engine to WordPress, as the default one is not very useful. Works out of the box, no settings, just install it and activate it.
There are already good plugins in the same area, so I've looked at all of them, and built some kind of 'mega-fork&mix', getting ideas and solutions from each of them.
The plugin exists in Lite / Pro / Ultimate editions, you can find more info on the WP-ISE official website.