To export your index data, you can use the “browse” feature from any of our API clients, as explained in the API documentation.
There is currently no way to export your index data directly from your Algolia Dashboard. The reason is that indices can be arbitrarily big (in the tens of gigabytes for example), which makes them not a good idea to download from a browser.
We're always looking for advice to help improve our documentation! Please let us know what's working (or what's not!) - we're constantly iterating thanks to the feedback we receive.