The only way to reach Komodo Island is by boat. The closest airport is the "Komodo" Airport at Labuan Bajo, on the island of Flores. Several airlines fly to Labuan Bajo from Bali. From Labuan Bajo, it is a two to three hour boat ride to the dragon viewing areas on Komodo or Rinca. You can negotiate to hire a boat or share one at the dock in Labuan Bajo. Boat rates run 750,000 to 1,500,000 Rupiah (45.00 USD to 90.00 USD) per day.
Alternatively, the inter-island ferry between Bima and Labuan Bajo stops at Komodo. There's only one ferry every two weeks, so this means either committing yourself to spending several nights on Komodo, or you still have to catch a private boat back to one of the ports.