I have backend code written in Java. The code has about 12 classes. However my partner on this project who is writing the interface (which uses Ajax) is more familiar with C# and .net. What would be quicker to learn Ajax with Java or to rewrite it in C#.
That's a big subject area you are opening up and you should go buy a couple of books and do some web research.
I got started with the Eclipse Web tools package and still use it. I was already using Eclipse for my Java development at the time so the transition was very smooth.
Edit: Holy crap you completely changed the question!
Straight Java and Ajax would involve some serious servlet programming. You'll probably want the aid of a web framework, i.e. JSP, Groovy, Tapestry, Wicket, Spring MVC, etc. Also, a Javascript library would help with the boilerplate AJAX and DOM manipulation stuff, i.e. jQuery or Prototype. The downside is that you'd have to invest time to learn these frameworks, though depending on the complexity of your Ajax, I bet you could get something running in a day or two.
If you have a standard Java servlet infrastructure and no surrounding framework, you may want to try out direct web remoting. It's an additional config/.jar in your web.xml
and little else on the server side.
It exposes nominated Java objects as Javascript objects automagically and makes enabling your Java domain objects in an AJAX environment very straightforward (trivial, in fact).
I've used this to migrate an existing servlet application to a more AJAX-focused solution and it works very well.
AJAX frontend should not know nor care about backend. Frontend sends requests to a controller and receives back JSON (XML,...) responses. Just download some decent AJAX javascript framework (there are lots of them - jQuery, Prototype, ExtJS etc) and it will handle all the low level communication stuff for you.