Search suggestions for Shopify

Add a search form to your theme:

<form action="/search" method="get" role="search" id="header-search">
<input type="hidden" name="type" value="product">
<label for="q">{{ 'general.search.placeholder' | t }}</label>
<input type="search" id="q" name="q" value="{{ search.terms | escape }}" class="input-group-field" />
<input type="submit" value="{{ 'general.search.submit' | t }}" class="input-group-field" />
</form>

Create a template called search.json.liquid

{% layout none %}
{% capture results %}
  {% for item in search.results %}
    {% assign product = item %}
    { 
      "vendor"    : {{ product.vendor | json }},
      "title"    : {{ product.title | json }},
      "url"      : {{ product.url | within: product.collections.last | json }},
      "thumbnail": {{ product.featured_image.src | product_img_url: 'thumb' | json }}
    }
    {% unless forloop.last %},{% endunless %}
  {% endfor %}
{% endcapture %}
{
  "results_count": {{ search.results_count }},
  "results": [{{ results }}]
}

Create this snippet and add to theme layout.

<script>
$(function() {
  // Current Ajax request.
  var currentAjaxRequest = null;
  // Grabbing all search forms on the page, and adding a .search-results list to each.
  var searchForms = $('form[action="/search"]').css('position','relative').each(function() {
    // Grabbing text input.
    var input = $(this).find('input[name="q"]');
    // Adding a list for showing search results.
    var offSet = input.position().top + input.innerHeight();
    $('<ul class="search-results"></ul>').appendTo($(this)).hide();    
    // Listening to keyup and change on the text field within these search forms.
    input.attr('autocomplete', 'off').bind('keyup change input propertychange', function() {
      // What's the search term?
      var term = $(this).val();
      // What's the search form?
      var form = $(this).closest('form');
      // What's the search URL?
      var searchURL = '/search?type=product&q=' + term;
      // What's the search results list?
      var resultsList = form.find('.search-results');
      // If that's a new term and it contains at least 3 characters.
      if (term.length > 3 && term != $(this).attr('data-old-term')) {
        // Saving old query.
        $(this).attr('data-old-term', term);
        // Killing any Ajax request that's currently being processed.
        if (currentAjaxRequest != null) currentAjaxRequest.abort();
        // Pulling results.
        currentAjaxRequest = $.getJSON(searchURL + '&view=json', function(data) {
          // Reset results.
          resultsList.empty();
          // If we have no results.
          if(data.results_count == 0) {
            // resultsList.html('<li><span class="title">No results.</span></li>');
            // resultsList.fadeIn(200);
            resultsList.hide();
          } else {
            // If we have results.
            $.each(data.results, function(index, item) {
              var link = $('<a></a>').attr('href', item.url);
              link.append('<span class="thumbnail"><img src="' + item.thumbnail + '" /></span>');
              link.append('<span class="title"><strong>' + item.vendor + '</strong><br >' + item.title + '</span>');
              link.wrap('<li></li>');
              resultsList.append(link.parent());
            });
            // The Ajax request will return at the most 10 results.
            // If there are more than 10, let's link to the search results page.
            if(data.results_count > 10) {
              resultsList.append('<li><span class="title"><a href="' + searchURL + '">See all results (' + data.results_count + ')</a></span></li>');
            }
            resultsList.fadeIn(200);
          }        
        });
      }
    });
  });
  // Clicking outside makes the results disappear.
  $('body').bind('click', function(){
    $('.search-results').hide();
  });
});
</script>

Reference: https://help.shopify.com/themes/customization/store/enable-autocomplete-for-search-boxes