How to get around Tokyo/the rest of Japan on a budget?

I'm a relatively experienced traveler who just purchased a one-way ticket to Tokyo. I'll be there for 10 days, starting December 27th (evening) and leaving sometime January 6th. I was wondering what are some ways to help stretch a dollar (or yen) in Tokyo. I'm looking for, in particular, public transport prices (or perhaps something similar to London's Oyster card), and ways to get around the rest of Japan for relatively cheap. Also, if you have anywhere else in Japan that you suggest seeing, or any special events going on in the dates I'm going, go ahead and answer with that too!