From 1989 to 1994 I studied Chinese at universities in the UK and Taipei. The variety of spoken Chinese I learnt was Mandarin and I learnt to read and write Modern Standard Chinese in both traditional and simplified characters. In addition, I'm familiar with a number of phonetic transcriptions systems: Hanyu Pinyin, Wades-Giles, Yale and Bopomofo, and have studied some Classical Chinese.
I speak Mandarin fluently and can write Modern Standard Chinese quite well, but am only able to have very basic conversations in Taiwanese and Cantonese.
Details of my experiences of learning Mandarin
While I was in Taipei I had a go at learning some Cantonese. With a copy of Teach Yourself Cantonese and some help from my Cantonese-speaking friends I managed to acquire a basic knowledge of the language.
In 1999 I tried to learn some more Cantonese to improve my chances of securing a job as a Chinese Student Advisor at the University of Luton. The textbook I used was Colloquial Cantonese, which is quite good, though I found the lack of Chinese characters in it somewhat frustrating.
I was invited for an interview for the Luton job, though by that time I had already been offered a job in Brighton. Having visited both Brighton and Luton the decision which to choose was not hard - the job in Luton might have been more interesting, but Brighton is a much more pleasant place to live, so I chose Brighton.
I still know enough Cantonese to understand it a bit and to have a basic conversation, but rarely have opportunities to use the language so haven't made any further progress.
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.
Welsh, French, German, Italian, Icelandic, Japanese, Portuguese, Mandarin, Cantonese, Taiwanese, Korean, Scottish Gaelic, Spanish, Esperanto, Hungarian, Turkish, Arabic, Czech, Irish (Gaelic), Latin, Manx (Gaelic), Russian, Urdu, British Sign Language (BSL), Hindi, Breton