Complex sentence: The Hugo Awards are voted on by science-fiction fans at the World Science Fiction Convention; the Nebula Awards--given by the Science Fiction and Fantasy Writers of America (SFWA)--began in 1966, making that the first year joint winners were possible.
Split into simpler sentences: The Hugo Awards are voted on by science-fiction fans (at the World Science Fiction Convention); the Nebula Awards are given by the Science Fiction and Fantasy Writers of America (SFWA). The Nebula Awards began in 1966, making that the first year joint winners were possible.