Citizens of the US and Canada do not require a visa or passport, but should carry a birth certificate or naturalization certificate with a picture ID to prove citizenship. British citizens need a passport but not a visa. Citizens of all other countries need a passport, and, in some cases, a visa. Visitors are permitted to stay for up to six months but must have proof of departure. Things are expensive and it is best to be prepared for that.
Food is pricey because most of it's imported, and accommodation is simply in short supply.
The majority of visitors to the islands sleep on chartered yachts. Bear in mind that renting one of these will cost a few paychecks. Coming in the low season will reduce room prices and charter rental fees, sometimes by as much as half. Strangely, the local currency is the US dollar, since the British Virgin Islands decided it was easier to stick with the same currency as its bustling US neighbor. Travelers' checks and major credit cards are widely accepted except on Anegada, where it's best to bring cash.