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jQuery.ajax(ajaxurl,{ //ajax url is not available in the front end. Needs to wp_localize_script
    data: {
      action: "", //the action specified in ajax wordpress hooks
      //other_param: new_value,
      //another_param: another_value
    },
    dataType: "json", //Default is an "intelligent guess"; does not work very often
    method: "POST" //Default is GET
}).done(function(data, textStatus, jqXHR){
    console.log(data);
}).fail(function(jqXHR, textStatus, errorThrown){
    console.log(errorThrown);
}).always(function(result, textStatus, type){
    console.log(type);
});