What are the basic principles for applying for a .TW domain name in English?
(i) Based on the first come first served principal.
(ii) The applicant can apply for more than one .TW domain name.
(iii) Applicant can choose respective .TW domain name for registration in accordance with the types of names and their requirements, and apply with respective

agencies.
(iv) Applicants should attach relevant documents for their application of respective type of domain name for screening.
How do I register a .TW domain name?
If .TW domain name that you intend to register is available, you should contact one of the authorized agencies (Todayisp.com). Many authorized agencies allow you to register .TW domain names with them immediately thorough automated functions on their web site. Before you register the .TW domain name, make sure you fully understand the authorize agency's terms and conditions.
What's next after I've decided on a .TW domain that not already taken?
You will then need to submit an application to Todayisp.com and provide the following information on the application:
1. The domain name applied for and the registration term.
2. The name, organization and other contact ways of the applicant.
3. The name, organization and other contact ways of the administrator.
4. Name server information.
5. Other information required by the Taiwanese authorities or Todayisp.com.

Source: http://rs.twnic.net.tw/