This snippet will display the latest post in a specified FeedBurner feed. Just set the URL to your desired FeedBurner feed.

$(document).ready(function(){
       $.ajax({
               type: "GET",
               url: "http://feeds.feedburner.com/examplefeed",
               success: function(data){
                       $("#date").text($(data).find("item:first>pubDate:first").text());
                       $("#title").html("<a href='"+$(data).find("item:first>link:first").text()+"'>"+$(data).find("item:first>title:first").text()+"</a>");
                       $("#description").html($(data).find("item:first>description:first").text());
               }
       });
});

This example assumes that there are 3 elements that this information will be sent to, with the ID attributes set to date, title and description respectively.