The final efforts that brought Allied victory in Asia consisted of moving closer and closer to Japan by conquering islands in the Pacific.  From these islands, the Americans were able to bomb Japan and, through the use of atomic bombs, destroy its ability to resist.

The major battles that were relevant in this regard were those at Saipan, Iwo Jima, and Okinawa.  By taking Saipan (and the adjacent island of Tinian), the US obtained bases from which to bomb Japan using B-29s.  Taking Iwo Jima and Okinawa made it clear that the US was going to be able to invade Japan and would likely be victorious.  What capped this process was the dropping of the atomic bombs from airplanes taking off from Tinian.