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 disturbing 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 helped Squidward clean up the trash pile in Bikini Bottom, Squidward happily returned home to continue along with his day. Unfortunately for him, he ventureed instead into a disgusting version of his house. He would actually drink garbage tea and even eat garbage toast. He then took a "shower" before finally going to bed.
It is when he smells the covers he discovered something was wrong and quickly runs out of his "house." He notices the trash house and demands SpongeBob to tell him where his house is. SpongeBob points out that Squidward's house is actually on top of the trash house.
A policeman (who is actually 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 askes 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 was washing himself in the garbage shower. It is possible it was just used for comedy.
Squidward did not recognize the dirtiness until he smelled the covers of his bed which ironically, is not necessarily worse than drinking garbage and showering in filth.