In Micronesia, the initial cleanup was done by captured Japanese soldiers when available, and American soldiers when they weren't available, sometimes including Islander labor as well. The immediate concern in bypassed islands (which didn't see land invasions) was removing dangerous ordnance, particularly mines, and identifying caches of bombs and other weapons if necessary. On islands with land invasions, the damage would have been more severe, and often there were fewer Japanese soldiers to do work because so many had been killed in battle. The priorities on those islands would have been similar, with most work being done by the much larger number of American soldiers on island for the invasion, but disseminating supplies and building temporary shelters would have been more necessary.

After the end of the war, the US Navy expended some effort (not enough, according to some) to reconstruct the basic infrastructure on larger islands that had been destroyed by the war. That included roads, harbors, quonset huts with all the stores and government offices the Navy thought necessary, and sometimes homes as well. The Navy also built a fledgling capitalist economy which it controlled, first through the United States Commercial Company and then the Island Trading Company.

Some of the ruins from the war were sold by Islanders for scrap metal. Other pieces are still there. Chuuk is a popular diving spot because of the large number of airplane and shipwrecks from the war at the bottom of the lagoon. It's common to find WWII tanks, cannons, seaplane ramps, concrete structures, railroad tracks, water tanks, and all sorts of other remants in the islands today as well.

As for bodies, the US military took care of its own dead. I'm less sure about Japanese military procedures, but I know the bones of many, many Japanese soldiers were left behind. Private Japanese "bone collecting missions" ramped up after the war as a way to recover some of those remains. They still occur occasionally; there was one in the Marshalls earlier this year, I believe.