If you are asking about building a URL, that can be sent to someone else, that will both (a) automatically display subtitle/caption and (b) make the transcript immediately visible below, for a particular language, eg, German, you can add this string behind a normal TED Talk URL:
/transcript?language=de
For example,
https://www.ted.com/talks/ken_robinson_how_to_escape_education_s_death_valley
becomes
https://www.ted.com/talks/ken_robinson_how_to_escape_education_s_death_valley/transcript?language=de
In your particular example, note that today it has been redirected to a URL with the parameter "?language=en". In this case, you need to replace "?language=en" with "/transcript?language=de" if the targeted language is German.
https://www.ted.com/talks/chimamanda_adichie_the_danger_of_a_single_story?language=en
becomes
https://www.ted.com/talks/chimamanda_adichie_the_danger_of_a_single_story/transcript?language=de
The actual language code in the above examples is "de". Other examples are "zh-cn" for Chinese Simplified, "id" for Indonesian, and "es" for Spanish.
How to find out more language codes?
On the general listing page (https://www.ted.com/talks), select the "Languages" drop down select list, then any of the videos, and its URL should end with something like "?language=ja" if you have selected Japanese in the drop down list. In this case, you've found that "ja" is the language code for Japanese on TED Talks site.
Not all TED Talks videos are translated. You can estimate the total number of translated videos in any language by looking at its listing page to see the maximum number of pages listed. Multiply the maximum page number by 36, as each page currently lists 36 videos.
