Taiwanese is a variety of Hokkien which is one of the Southern Min languages which in turn belong to the Sinitic languages. Taiwanese is widely spoken in Taiwan next to Mandarin, Hakka and a variety of indigenous languages belonging to the Austronesian language family (languages of Taiwan).
Catherine Chou | Catie Lilly has collected an impressing amount of information on twitter for people who want to learn Taiwanese 台語 Tâi-gí from English. Central is this document with a lot of valuable links for language learners.
I picked out a few of them:
Bite Size Taiwanese podcast and textbooks
Taiwanese Made Easier textbook
Maryknoll Taiwanese-English Dictionary
chhoe.taigi.info aggregates 7 different Taiwanese dictionaries & allows searching in 台文, Mandarin, POJ Romanization & English
PhahTaigi 台語輸入法 (Taigi Keyboard) for Android
Chrome extension with helpful tools for studying Taiwanese
In the document you'll find information on courses both online as well as in person and a lot of additional info. Learning (some) Taiwanese is certainly worth of consideration if you're going to spend some time in Taiwan and moreover it's a very interesting language. All the credits to Catherine Chou who has put a lot of effort in establishing this treasure trove and who also tells about her personal language journey.
Lastly I'll add a song in Taiwanese: 葬予規路火烌猶在 by 珂拉琪 Collage. You can find the lyrics here (歌詞 click > ...查看更多).