Just did this last night with Mother's and a paper towel.Mother's Mag and Aluminum polish is the product. In the display case discussion I did a review of it compared to some other products once upon a time. If you're interested you can probably find it by searching "polish review" posted by me in that forum, but basically Mother's really put a shiny polish on things, even if that wasn't the original finish.
"Elbow grease" - you'd asked "the best way"... Using Mothers you just need a clean cloth and do it by hand i.e. elbow grease; no need for a dremel or other fancy tool...