I don't think it's possible to discuss all the themes in "Bride Comes to Yellow Sky" "exactly," but I can give you a few ideas about the main ones.
The story's main theme, I think, is the inevitability of change. Crane looks at the passing away of the old and the emergence of the new through the characters of the Sheriff and his "nemesis" Scratchy. Scratchy and the Sheriff have been doing things the exact same way since they met - living in a town that has been exactly the same for a long time. Now, two major things have happened: the railroad is coming through, which certainly indicates that things will never be the same, and the sheriff has gotten married.
Scratchy, who hasn't changed, is confounded by this fact when he encounters the sheriff and his new bride.
The story is also about communication and the way we deal with others, but the main theme of change does predominate.