Some senior citizens still speak Japanese as the result of Taiwan being part of Japan from 1895-1945.
You may be surprised to find many locals being able to adequately communicate with you in English, especially in the case of the younger generation. Both the government and people have devoted considerable resources to the learning of English in trying to "internationalize" Taiwan. Although the bulk of English language learning starts at junior-high, even grade school students have learned some amount of English either at school or at a so-called "English-only" day care center. Therefore, do not hesitate to ask for help in English. Even if the local cannot speak English, he/she will try his/her hardest to help you. Consult the English Wikipedia article on Chinglish to understand the greatest challenges locals face in communicating in English.
Unlike Mainland China, you may find the Chinese romanization for the names of streets and places in Taiwan to be inconsistent and therefore confusing. A same road may have various kinds of romanized spellings, tricking you to think that you have not reached your destination when in fact you have.
In 2002, the national government created a paradox policy as a compromise to the politically sensitive issue of Chinese romanization in Taiwan. Although the ROC government adopted Tongyong Pinyin as the national romanization system, it allowed local governments to decide what system to use for their own locality. Taipei has adopted Hanyu Pinyin, replacing earlier signage, most of which had used a hybird mixture of the Wade-Giles system and the Chinese Postal Map Romanization system. Kaohsiung, Taiwan's second-largest city, has adopted Tongyong Pinyin. Elsewhere in Taiwan, signs tend to be a mixture of different systems, with the MPS2 frequently encountered. Romanization errors are common throughout Taiwan because a Chinese-character based phonetic alphabet rather than the Latin alphabet is used in schools to teach Chinese pronunciation, and there is little political will for consistent implementation.
The English Wikipedia article on the Comparison of Chinese romanization systems provides a conversion table between the different systems. It is generally safe to assume that if two signs have vaguely similar spellings, they should refer to the same location. Nevertheless, it does help to bring a notecard containing the Chinese characters of your final destination and to compare these characters with the signs.
Regardless of the romanization system, there is some disagreement on whether conversion of Chinese words into English should be done completely as a phonetic transliteration or as a mixture of phonetic transliteration and literal meaning. Take the Yangmingshan National Park as an example. It is literally "Bright Mountain" in Chinese. However, Yangming is actually the name of a person, so it would make sense to call the place "Yangming Mountain" in English. However, "Mountain" is "shan" according to most romanization systems; therefore the place could also be called in transliterated English as "Yangmingshan." Locals would probably know what you are talking about if you said "Yangmingshan" rather than "Yangming Mountain" in English.
If you are highly interested in learning Chinese, please visit the common phrases page, which we especially created for you.