If you are from one of the countrys wich have a Working Holiday Visa agreement with Japan than you can! America is not one of this Countrys!
But english speaking countrys include New Zealand, Australia, Canada, Uk and Ireland. Other than that: Germany, France, Denmark and South Korea
Its funny how people assume that its impossible for everyone just because its impossible for Americans. I know that most ppl on this forum are Americans, so Nyorin gave a good answer for most people but i thought i posted about this Visa before...
Edit: Just checked your profile and saw youre from Canada
have a look here
Embassy of Japan in Canada - Working Holiday Visa Requirements for Canadian Citizens If you are really going, send me a message, i can send you a link to a place where you might get something to get started.