Raja Ampat is served by Domine Eduard Osok Airport in Sorong. The easiest way to get here is to fly directly from Bali, Jakarta or Makassar.
Once you arrive in Sorong, hail a Grab or motorbike to the ferry harbour. There, you can hop onto public ferries and boats that head to the various islands, but note that the ferries don't run daily. For more flexibility, ask if your accommodation can arrange a private speedboat transfer.