How to Clean a Shinken: Two Methods
This video describes two methods of cleaning a shinken -- a katana with a live blade.
The modern method, which some feel is less abrasive, uses isopropyl alcohol and a micro-fiber cloth. The traditional method uses uchiko powder, a mild abrasive, and sword-cleaning paper. The video also has some tips on how to oil your blade.
Standard dojo etiquette disclaimer: If your sensei teaches you a different way, please follow your sensei's instructions.