Complex sentence: At the beginning of each show Jim Henson would come out with the white lion from The Storyteller to indroduce the show and the second half, which was either an episode of The Storyteller or a half-hour special.
Split into simpler sentences: At the beginning of each show, Jim Henson would come out with the white lion from "The Storyteller" to introduce the show. The second half was either an episode of "The Storyteller", or a half-hour special.