Wakatobi is well known among divers as one of the world's best dive sites. The name is an an acronym of the four component islands: Wangiwangi, Kaledupa, Tomea, and Binongko.
Most travel to Wakatobi departs from Kendari and arrives in Wangi-Wangi, either by boat or plane. The first commercial flight was on October 30th, 2012 by Wings Air, a subsidiary of Lion Air. There are plans for Merpati to fly there as well. Be aware that the airport is on the exact opposite side of the island than the only city and there is no public transport available. If you've booked ahead at a resort they will probably have someone waiting for you. Otherwise someone at the airport can call a taxi or ojek for you and you will likely have to wait 30min for it to arrive before starting your 30min journey into town. An ojek costs RP 50,000.
From Bau-Bau: 3 flights per day between Makassar (Ujung Padang) and Bau-Bau. Bau-Bau is a lovely city which hosts the head office of Wakatobi National Park. It's well worth a few days visit on its own, with an amazing 16th century fort, white sand beaches with nice coral snorkelling, and lots of caves. Slow boats to Wakatobi National Park depart from Bau-Bau most days and take about 9 hours (overnight) to reach the nearest island, Wangi-Wangi. The Cantika fast boat departs Bau-Bau every 2-3 days around 10am and arrives in Wangi-Wangi around 2pm before continuing on to the islands of Kaledupa and Tomia. Fast boat costs about Rp250,000 from Bau-Bau to Wangi-Wangi and is very safe and comfortable. Check the schedule a few days before you arrive in Bau-Bau.
Most divers arrive in Wakatobi via the Wakatobi Resort's scheduled chartered flights from Bali.
For independent travel, the Cantika fast boat connects the main islands of Wangi-Wangi, Kaledupa and Tomia on a rolling schedule, so going each direction every 2-3 days. There is no shortage of smaller boats connecting the various islands, so on any given day you should be able to move from one island to another. It's best to just ask around (for example, at your accommodation reception) a day or two before you want to travel.
On the main islands, ojeks (motorcycle drivers) are easy to flag down on any main road or harbour and usually cost around Rp5,000 for a short trip, such as from a hotel to the harbour.