you have to first landed at Sorong. try google these airline: merpati, batavia air, lion air, sriwijaya air, express air.
the cheapest way is by ferry which will take off to waisai (capital of raja ampat) at 14.00 everyday.
then try to find hotel there and ask the hotel to arrange your next day trip.
but since now there are many local tour to raja ampat in sorong, you can first arrange with them.
many of traveller i've met here (sorong), they complained so much about the price. expensive (and i agree)
but still we can make the trip affordable. don't worry almost 6 years ago