CakePHP中的$ _POST相当于ajax调用？

Normally, when I'd do an ajax call to a page with jQuery's $.post(), I'd post to a specific page (i.e. ajax.php) with something like:

var submissionId = 1;
$.post('/ajax/ajax.php', {
        submissionId: submissionId
}, function(data) {
alert(data);
});

and inside ajax/ajax.php, I'd manipulate the data how I'd want with $_POST['submissionId']. What is the equivalent to this in CakePHP if I'm posting to a controller?

Do I still use $_POST['submissionId'] or $this->data?

If using $this->data, do I need to create a <form> to wrap the event handler in?

you should create form with cake helper (hide it with css or jquery if you don't want it to be there) and use jquery form plugin
you can submit the form with jquery with submit()
so in the controller you can use $this->data