I don't know enough about it to write myself, but the 'Speak Mandarin!' campaign in Singapore is an interesting example of language standardizing where the local dialect of Chinese was not Mandarin.
It is hard to standardize on a dialect. People in Hong Kong speaks Cantonese. But when they knew about 1997 couple decades ago, people started taking Mandarin classes on their own. Many grade schools and high schools started to include Mandarin as one of the subject. It is now almost 20 years since the talk about China taking back Hong Kong in 1997, Cantonese still is the dialect people speak in Hong Kong. However, many more people, especially the young and educated, know Mandarin.