One way to go is to book a flight with Ryanair to Frankfurt, this means ending up at Frankfurt-Hahn a regional airport, somewhere halfway between Frankfurt and Luxemburg. According to their website, there are busconnections to Luxembourg from this Airport http://www.flughafen-hahn.de/default.aspx?menu=by_bus&cc=en Only note that the flights leaves Milan, from Bergamo airport. Check Ryanair for the connections to this airport. Easy ... not really?
Another option is to again take a flight from Bergamo, but this time to Brussels (or what Ryanair calls, Brussels) this is in fact Charleroi, again not too far from Luxembourg. But it will still take you a couple of hours to get from Charleroi to Luxembourg. Easy ... not really?
Going by train is also not the easiest, and will take pretty long. According to Bahn.de, at least 15.5 hours, with several stopovers.
[ Edit: Edited on Dec 17, 2008, at 4:09 PM by Herr Bert ]