How can I send an Ajax Request on button click from a form with 2 buttons?

Given that the only logical difference between the handlers is the value of the button clicked, you can use the this keyword to refer to the element which raised the event and get the val() from that. Try this:

$("button").click(function(e) {
    e.preventDefault();
    $.ajax({
        type: "POST",
        url: "/pages/test/",
        data: { 
            id: $(this).val(), // < note use of 'this' here
            access_token: $("#access_token").val() 
        },
        success: function(result) {
            alert('ok');
        },
        error: function(result) {
            alert('error');
        }
    });
});