The IMDb summary ties up all the plot's various loose ends better than I could:
1949, Santa Rosa, California. A laconic, chain-smoking barber with fallen arches tells a story of a man trying to escape a humdrum life. It's a tale of suspected adultery, blackmail, foul play, death, Sacramento city slickers, racial slurs, invented war heroics, shaved legs, a gamine piano player, aliens, and Heisenberg's uncertainty principle. Ed Crane cuts hair in his in-law's shop; his wife drinks and may be having an affair with her boss, Big Dave, who has $10,000 to invest in a second department store. Ed gets wind of a chance to make money in dry cleaning. Blackmail and investment are his opportunity to be more than a man no one notices.
What a cast! It's seems as if everyone wants to work with the Coens. You've got Billy Bob Thornton, Frances McDormand (of course married to Joel Coen),