I am an Indian, working in Shanghai, China. I need to travel to Taiwan for a short visit of around 10 days. How can I get a visa for Taiwan?
As China considers Taiwan to be part of China, there is no embassy or consulate through which to apply for a visa.
The first option would be to apply at a Taipei Economic and Cultural Center in your home country. You may be able to do closer to your current location, such as in Hong Kong or Singapore (or through a travel agency in either).
Taipei Economic and Cultural Office (India)
No. 34, Paschimi Marg, Vasant Vihar, New Delhi, Phone: +91 11 4607 7777
Taipei Economic and Cultural Office (Hong Kong)
Lippo Centre, 89 Queensway, Tower 1, Room 1106, Phone: 2525.8316
Taipei Representative Office (Singapore)
460 Alexandra Road, #23-00 PSA Building, Phone: +65 6278 6511
An added observation by @dda, to whom thanks, Hong Kong would be a better option as Indian nationals only need to pre-register, rather than the visa required for Singapore (as well as the flight time).