If you are going to be in the FSM for less than 30 days you do not need an entry permit. Anyone who will be staying longer than that needs an entry permit.
For citizens of the Marshall Islands, Palau, and the United States/American Samoa, entry permits lasts 1 year. Additionally, citizens of the mentioned jurisdictions can also opt to show their birth certificate as proof of nationality for entry, instead of a passport.
For everyone else, entry permits lasts 30 days, but can be extended to 60 days. You can get your entry permit on arrival, but if you're travelling for a purpose other than tourism, you need to apply for it in advance. Most people will need to prove their citizenship with a passport or travel document that has at least 120 days of remaining validity. If you need to apply for an entry permit on arrival, you must present an FSM Arrival and Departure Record. This is furnished by a carrier before entering the FSM. You will need a completed application form in addition to this.
The major airline that travels to FSM is United Airlines, which operates a thrice-weekly "island hopper" flight UA155 eastbound, UA154 westbound traveling Honolulu—Majuro—Kwajalein—Kosrae—Pohnpei—Chuuk—Guam and vice versa. The flight is fourteen and a half hours, leaving in the early morning and terminating in the evening, with a stop of about one hour on each island. There are also nonstop flights from various islands to both Honolulu and Guam.
Honolulu is the most direct gateway into the islands from North America. Guam is the most direct gateway from most points in Asia and Australia, although it is also possible to fly into the islands from Manila via Palau.