The outside of Squidward's trash house appears to be a replica of Squidward's regular house and even appears to be the same size but instead covered in trash.
The interior of the trash house is very disgusting and resembles Squidward's actual interior of his house. It has many rubbish features, including a trash toaster, trash bread, a trash teapot and teacups, a trash shower, and even a trash bed.
After SpongeBob helps Squidward clean up the trash pile in Bikini Bottom, Squidward happily returns home to continue along with his day. Unfortunately for him, he ventures instead into a disgusting version of his house. He drinks garbage tea and eats garbage toast. He then takes a "shower" before finally going to bed.
Once he smells the covers he discovers something is wrong and quickly runs out of his "house." He notices the trash house and demands SpongeBob to tell him where his real house is. SpongeBob points out that Squidward's house is actually on top of the trash house.
Officer John Slugfish (the same policeman who has been giving tickets to Squidward for the entire episode) gives Squidward a ticket for having the filth. Squidward gets angry and asks SpongeBob to get rid of the trash.
SpongeBob goes on to tell Squidward that the Dump was closed and that explains why he built the house and why Squidward's actual house is on top of a giant replica of Squidward's house made of trash. SpongeBob uses his body to suck up the trash house, thus getting rid of it as Squidward's real house drops back into place.
It is unknown how SpongeBob even got or built the trash house under Squidward's house.
It is also unknown how Squidward didn't notice the trash house right away, especially after drinking the garbage tea and even when Squidward is washing himself in the garbage shower.
It is possible it was just used for comedy.
Also, when Squidward was drinking the garbage tea and eating the garbage toast, he opened his eyes, so he should've seen the trash. Once again, it is possible that it was just used for comedy.
Squidward does not recognize the dirtiness until he smells the covers of his bed which, ironically, is not necessarily worse than drinking garbage and showering in filth.