Chinese cultures worldwide have a rich history in fortune telling and spiritual methods of influencing the world around them. Taiwan is no exception, and fortune telling abounds in Taiwan.
Methods vary widely, from the well-known Feng Shui (geomancy) to the I Ching (divination by eight diagrams) to divination by features of the face. There is even Chinese palmistry - similar and yet very different from it's Western counterpart. In the links above we have basic details on the most common forms to be found in Taiwan.
For the tourist, Chinese fortune telling is a fantastic way to have a truly unique Taiwan experience. Night markets, especially the fixed, main ones, offer a variety of different fortune tellers. Additionally, sometimes they can be found with tables set up on the street. Some, especially those specialising in areas particularly important to weddings and business (like Feng Shui) have offices. For most tourists, the easiest way to find a fortune teller is to visit one of the nightmarkets, preferably with a local to assist in translating.