How did US get rights to build panama canal?

A good question. The country of Panama had been part of the nation of Colombia. The United States brought great pressure to bear on Colombia to grant independence to Panama, at the same time negotiating with Panamanian entities for rights to build the canal. Given these factors, it's reasonable to say that Panama granted the US a long-term lease to build, operate, maintain and control the Panama Canal as a quid pro quo for its independence.