The same as cash income - primary way is that you report it yourself; secondary way is auditing suspected violators, possibly involving policework.

"Anonymous" in the sense of "broadcast to the entire network."

but all transactions are public [1] Thus once you inform gov which are your bitcoin wallets, they can look through the block chain. Ironically, this means they will have much much more info on you than if they just had your bank account number.

[1] https://en.bitcoin.it/wiki/Transactions

It's anonymous until you exchange your Bitcoins for Euros/Other currency.