how to set ajax auto-complete text box set of with java script

You would need to implement AJAX using the XmlHttpRequest ie XHR object.
Steps.
1. Place a div next to the text box
2. Implement observer for onchange, and call the XHR routine ( implement your-own using raw object or utilize the industry standard JQuery or the YUI java script library)
3. On success of the call, place the result of ajax in innerHtml of the attached div used for dropdown - from Step 1)
4. On the div as well, place a observer for the on-click for selection and later populating the textbox and hiding the div
 
And ... This should be done