To handle AJAX requests using jQuery, you can use the jQuery.ajax() method. This method is used to perform asynchronous HTTP requests and can handle different types of responses, including HTML, JSON, XML, and text.

Here's an example of how to use jQuery.ajax() to handle an AJAX request:

$.ajax({
 url: 'example.com/api/data',
 type: 'GET',
 dataType: 'json',
 success: function(response) {
   // Handle successful response
   console.log(response);
 },
 error: function(xhr, status, error) {
   // Handle error response
   console.log(error);
 }
});

In this example, we're performing a GET request to 'example.com/api/data' and expecting a JSON response. We've also defined success and error functions to handle the response.

The success function will be called if the request is successful and will receive the response data as an argument. The error function will be called if there is an error and will receive the XMLHttpRequest object, the status of the request, and the error message as arguments.

You can also use other shorthand methods like jQuery.get() and jQuery.post() for GET and POST requests respectively, which provide simplified ways to send requests and handle responses.