Sample to code call REST API from visualforce page

VFRestAPI.html

<apex:page>
  <apex:includeScript value="https://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.7.2.min.js"/>
  <script>
    jQuery(document).ready(function($) {
      // Pull 10 Contacts via the REST API
      $.ajax('/services/data/v28.0/query?q=SELECT+Name+FROM+Contact+LIMIT+10',
        {
          beforeSend: function(xhr) {
            // Set the OAuth header from the session ID
            xhr.setRequestHeader('Authorization', 'Bearer {!$Api.Session_ID}');
          },
          success: function(response) {
            $.each(response.records, function(index, record) {
              //Add your logic 
            });
          },
          error: function(jqXHR, textStatus, errorThrown) {
            // Display error message
            alert(jqXHR.status + ': ' + errorThrown);
          }
        }
      );
    });
  </script>
  <h1>Test REST API Without Proxy</h1>
</apex:page>