East Asian Costume is a somewhat broad topic so it might be best to do research by a specific country or ethnic group. If you do want an overview on the topic though here are some suggested search terms to use in OneSearch:
Ethnic costume
Ethnic costume -- History -- Pictorial works
Costume-- Asia
Costume-- East Asia
Fashion-- Asia
Textile fabrics-- Asia
Textile fabrics-- East Asia
Cross-cultural studies
Silk-- Asia
Silk -- East Asia
Embroidery-- Asia
Embroidery -- East Asia
Books about East Asian Costume can be in a number of different sections of the library depending on if the book's focus is textile type, time period, art by country or individual designer. Here are some suggested call numbers to start browsing:
GT 511- Modern Fashion
GT 525- Fashion, cultural aspects
N 7336-7369- Art, East Asia
NK 8883-8884- Textile arts, East Asia
NK 9200- Embroidery
TT 505- Designers
(TT505 is a HUGE section! Try to find the specific number for an individual designer by searching their name in OneSearch. For example most books about "Guo Pei" will be under TT505.G86.)