US citizens equipped with a valid passport and an onward ticket can visit American Samoa visa-free. Nationals of Australia, New Zealand, Canada, the UK and some EU countries equipped with a passport (valid for at least 60 days) and an onward ticket will receive a free one-month visa on arrival. Other nationals must apply in advance for their one-month visa (US$40). It's a good idea to check your status before you go.
Visas can be issued by the Attorney General's office, but given that it has no official website, email queries often go unanswered and the phone connection can be dodgy, it's a better idea to ask your hotel if they can arrange a visa for you (fee about US$40).
Visa extensions are handled by the AG or the Immigration Office, located within the government building in Pago Pago. Visas can only be extended by one month; the fee for this varies depending on what country you hail from. Again, larger hotels should be willing to play the middleman in what can be a confusing and convoluted procedure.