How can citizenship be forfeited?

By renouncing your citizenship before a US embassy/ US consulate official. The US will not accept a renounciation if the government believes the renounciation was specifically performed so that the person can avoid paying income taxes (a US citizen/permanent resident is taxed on all WORLDWIDE income). If the government believes the renounciation was done to avoid taxes, the IRS will still tax you as if you were a citizen for 10 years after the renounciation.