Despite a recent plunge, bitcoin has had a banner year. Now comes the hard part—figuring out the taxes on it.

For the uninitiated, bitcoin is the most prominent of several "virtual currencies"—money that exists only online and isn't backed by any government. Released in 2009 by an unknown person or group going by the name Satoshi Nakamoto, bitcoin is maintained by a decentralized network of computers, called "miners," that process and verify transactions. As of Friday afternoon, the value of all bitcoins...