In Taiwan about 80% of the people speak Taiwanese. Most people also speak or at least understand Mandarin, though some don't. While studying and working in Taiwan (1993-1998) I sometimes had to communicate with people in Taiwanese and found the little Taiwanese I managed to learn very useful. I also have a number of Taiwanese-speaking friends.
I learnt Taiwanese through the medium of Mandarin using a textbook called Sing-wa Dai-ngi ("Living Taiwanese") which I think is only available in Taiwan, and with some help from Taiwanese-speaking friends. I also heard people speaking Taiwanese every day, as well as on the radio and TV, so became accoustomed to the sounds and rhythms of the language and can understand it to some extent, though can't speak it very well yet.
Occasionally I chat to Taiwanese people on Skype in a mixture of Taiwanese, Mandarin and English.
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