What is the best way to sharpen the blades on a cylender mower.

Do you mean a gas mower ? You would sharpen the blades the same way you do on an electric mower; I use a file or if they are really dull I take them off and get them sharpened professionally.

Are you speaking of a reel type mower? If so they do need to be professionaly sharpened. Don NOT try it with any other means.
Don