In the poem's first two stanzas, the speaker outlines the problem: life stinks because he has to work too much, "just for paying a few bills." As the poem begins, we also see what that amphibian title is all about. Larkin uses the image of a slimy, old toad to represent the work he so desperately wants to escape. Sorry toad-lovers, this one isn't actually about our amphibian friends.
For the next three stanzas, our speaker gives us examples of folks that seem to have beat the system, escaped that slimy toad work. The list includes "lots of folk [that] live on their wits," like conmen, and the unemployed poor.
The poem's final four stanzas show the speaker coming to terms with the fact that the toad is inescapable. It turns out that he has something "toad-like," something oppressive, in him as well, preventing him from feeling fulfilled. With the realization that he's dealing with internal as well as external toady-ness, the speaker resigns himself to life with his slimy nemesis.