I follow you.
I have an upcoming chat calendar setup on one of my international forums and it includes what date/time the next chat will occur, using the client's timezone offset to display the start time as per their time zone. I opted to do this instead a real time clock. You can store the time in a database and script a solution to query the database and generate the JS dynamically so the user would see "Next chat at 1/23/2008 12:34PM EST" (example).
Just an informal suggestion.
I can't offer advice on AJAX "specific to your needs" as I agree with the other user, you don't need AJAX to display a real time clock. But for retrieving any value from a DB via AJAX for whatever purpose you want, read below.
For general AJAX tutorial:
http://www.w3schools.com/ajax/default.asp
If you happen to be using PHP, I use Ace for AJAX - it involves working with PHP object oriented coding, i.e. classes. This is an advanced technique that allows you to create your own classes in PHP and work with a result function, percent completion function and a great error trap function with your data passed as arguments. It also requires declaring all argument variable types to stop SQL injection and hacking techniques which AJAX is vulnerable. This is a resource efficient open source solution using OOP (object oriented programming) alongside JS.
This means incredibly powerful and fast as well - a professional solution.
It's up to you to create the scripts to store the chat start time, check for DST, update the DB, and later in your scripts use AJAX to query the DB, parse and format the time for human readability, and display it in place in a div which calls the JS function which invokes ACE.
Details (membership is free to phpclasses.org) for ACE are here:
http://www.phpclasses.org/browse/package/3308.html
ACE makes doing all the above one integrated class package - so long as you know how OOP works with PHP of course. If not, start with the general tutorial and go from there.
-jim