Search as you type is user friendly and easy to implement with Ajax Search Lite, a highly customizable search plugin, that searches post, pages and custom post types, if you want it to. A few styles are included in the lite edition, with even more options in the pro.
Demo
The search field can be inserted anywhere on the page or in a widget using a shortcode.
Extract from WordPress.org
Ajax Search Lite is a live search plugin for WordPress. This responsive live search engine, which will boost your user experience by providing a user friendly ajax powered search form – a live search bar. You can filter the results with the category and post type filter boxes as well. Google autocomplete and keyword suggestions also included.
https://wordpress.org/plugins/ajax-search-lite/