There are currently no international airlines servicing Phu Quoc so if you are coming from overseas you will have to stop in mainland Vietnam first (note: construction of an international airport on the island is planned, land is set aside, and work will probably start soon.) Vietnam Airlines flies to Phu Quoc up to 11 times a day from Ho Chi Minh City (departing early morning to early afternoon, the most flights at the busiest times of the year) and Rach Gia (departing 7.50am). Rach Gia is the capital city of Kien Giang Province, which has jurisdiction over Phu Quoc. Return tickets to Phu Quoc can be bought for as low as US$30, although it depends on the season (US$80 seems a more reasonable estimate.)
Apart from flying, the only way to reach Phu Quoc is by sea. Most ships arrive in Phu Quoc at the southern port of An Thoi, although some land at Duong Dong. The journey generally takes two and a half hours from Rach Gia, and one and a half hours from Ha Tien. Operators running the Rach Gia route include the Duong Dong Express, a Norwegian built catamaran with air-con, reclining seats and panoramic views of the ocean crashing by. Tickets go for 250,000 Dong for adults, 170,000 Dong for children.
The Superdong Express hydrofoil is priced a little cheaper and is able to transport your motorcycle if you are riding one! Other boat services include Trameco, Hai Au (Seagull), Vietrosko Hydrofoil (sometimes unreliable) and the Bien Xanh (Green Sea) Express. The Bien Xanh Express costs about 180,000 Dong for the crossing.
Travel agents in Ho Chi Minh City can sell you combined bus/ferry packages to Phu Quoc. If your bus drops you off in Rach Gia you might be swarmed by motorcycle touts offering to take you down to the ferry. Since many bus services operate a free shuttle from the bus stop to the ferry, don't let the touts take you for a ride. You can get there for free. When you arrive on Phu Quoc you will probably be swarmed by touts once again. Go with the flow, because sometimes the touts can be your friend!
Coming from Cambodia
Cambodian territory might be visible from northern Phu Quoc, but as yet there are no direct air or sea connections. See the post on Sometimes 30 Equals 200 for insight into the absurdity of this. Things will change sooner or later (Cambodia is banking on it, as a direct link could drive tourists to its own coastal resorts), and Ganh Dau has been touted as Phu Quoc's potential gateway to the Khmer homeland. In the meantime, coming from Cambodia you will have to cross the border at Prek Chak/Xa Xia, present your Vietnamese visa, then go to Ha Tien and catch a ferry. It is complicated now, but things will probably get easier in the future.