I am looking for a science fiction book that is about an octopus who gains intelligence. That is all I know about the story and I have no idea when it was written but I'm thinking it's quite old.
This is possibly Jack Vance's The Gift of Gab. A mining operation of sorts -- the workers gather sea creatures that sequester valuable metals (based on the fact that Earth tunicates actually do this for vanadium).
One species of these organisms, the dekabrachs, are ten-armed creatures that the protagonist deduces are intelligent, but have no language. To save them from being harvested for a valuable metal, either platinum or palladium, he invents a language based on arm positions and teaches it to a captive dekabrach. The manager who discovered that the dekbrachs could be harvested attempts to poison the educated dekabrach with acid, but the dekabrach survives and is able to identify the attempted murderer.
At the end of the story, the captive is released, and it brings a number of other dekabrachs back to the operation to learn the new language.