I've tried three main methods of meeting women in Taipei. 1) Nightlife, 2) Introductions, 3) Online.
But first, some background. There is a huge, I mean HUGE pool of single available women in Taipei. Especially educated, professional women. The average Chinese/Taiwanese guy, is at best, an unintentional misogynist by western standards. Because of this, many, many Chinese/Taiwanese women refuse to destroy their quality of life by marrying one (Taiwan and Singapore depend on importing massive amounts of foreign brides to satisfy the demand for women who will marry a "traditional" Chinese/Taiwanese guy).
The problem is how to find this huge pool of single women. You may or may not feel comfortable with nightlife (bars, clubs, etc.). Certain bars and clubs have a reputation for being a place where local women go to meet foreign guys. You can ask other people here which ones are the most popular at the moment.
The second method, my favorite, are introductions. The Chinese/Taiwanese love to match-make. This is social-networking on speed with romance thrown in. Just let your work mates, class mates, teachers, and basically everyone in your professional and social circle know that you are looking for a girlfriend (you MUST do this in a respectful, courteous manner). They will carefully check you out over a period of a couple months (to make sure that you're not crazy) and make introductions for you. This is the standard, culturally acceptable way to meet women in Chinese culture.
The third method is online. The unfortunate thing about online is that all of the good online dating sites are in Chinese. However, there are some in English, such as TeaLit and ForumosaFriends (which is actually partnered/hosted by a wider global matchmaking site). The advantage of the English language sites is that the requirement for English pre-selects for women interested in foreign guys.
Don't worry about having no experience with dating. Chinese/Taiwanese men rarely hit on women due to shyness. Chinese/Taiwanese men also care little about their own appearance and live in a male-dominated society. This means that if you take care of your appearance, observe basic personal hygiene, and are courteous to women (the basics of western courting) you are already miles ahead of the local competition.
The variables and probabilities are too numerous to cover, but any respectful, polite, clean white male in decent phyical shape with a solid job should be able find anyone from a girlfriend to a wife in the male paradise of greater China.