Look to your right------> (where it says Get Started)
Api is a REST implementation and as such has no 'download'
You may access it right from your browser address bar or leverage one of the many client libraries that have been implemented.
List of API client libraries grouped by programming languageList of API client libraries grouped by programming language
If you are using JavaScript or C#, I would be remiss, as a library author, not to recommend the Soapi family of client libraries, but most all implementations are high quality.