One can only make very loose guesses regarding plot of WCITTS: it's incredibly abstract and one may argue that there is no plot at all. However, my analysis is as follows:

The protagonist is following the Darkness Fish, a being that looks to end existence. Their trek is not across the globe, but spanning points in time and planes of reality. However, the narrator/protanonist is quickly distracted by images of his past and his personal regrets. A recurring theme is his agony regarding miscommunication; "He couldn't get the voices out of his mishapen head... he couldn't get the voices out of his mishapen head," he groans on Landed at Granma's. After a stretch of nightmarish soundscapes, the main character is brought back to reality on Yagga Blues in which he remembers his original intent of stopping the Darkness Fish: "I quietly looked up to watch the transparent God-fish," he chokes amidst the twisted beat of bongos. "It had appeared again and it began to swim circles through the air. On several seperate occasions, she tried to communicate," the final line an allusion to his ongoing angst regarding speech.

On Livin' Fear of James Last, the narrator's fate is revealed: "I pushed the red button," he admits against the antagonistic sound of an air raid siren.
"With everything happening, I locked myself away in fear..." he cooly states as the music again degrades into bizzare, nightmarish territory. It is clear that when the narrator said "I pushed the red button", he meant that he caused the apocalpyse he was trying to stop the Darkness Fish from creating.

After several bizzare instrumental turns, the plot is picked up on Home Is Where the Heart Is. The narrator recalls seemingly unrelated incidents in his past, about a man he met who had beautiful eyes, about how he had once locked himself out of his apartment. Unfortunately, he transitions into quips regarding horrific casualities: "For a brief moment, no one died," he remarks apparently out of nowhere. "There would have been more death, if it wasn't for the birds..." he states regretfully later on. "Home" ends with him murmuring something about being "so far from home"... On this track his life flashes before his eyes as he "locks himself away", while darkness envelopes the world and reality is torn apart in unspeakable ways.

At the very end of final track, the narrator speaks against complete silence: "So I returned to the body that had never been my own. So far from home, am I."

Obviously the album is intended to be taken in many different ways. This is simply my interpretation.