MTR
The best MTR stations for transport to HKUST are: Choi Hung, Hang Hau and Po Lam. 
If you are traveling from the Hong Kong International Airport by Airport Express, go to Kowloon Station and take the MTR to either of the above stations. From either of them, you can then board a bus, minibus, or taxi that lets you off at the main entrance of HKUST.  

Bus/Minibus
Most of buses to HKUST leave from different MTR stations and bus terminals: 

Buses let you off at main entrance: 
From Choi Hung MTR station: 91 or 91M bus (use Exit C2); 11 minibus (use Exit C1)
From Hang Hau MTR station: 11M minibus (use Exit B1)
From Tiu Keng Leng MTR station: 792M bus (use Exit A1)
From Sai Kung bus terminus: 792M bus, 12 minibus

Buses let you off at southern entrance: 
From Hang Hau MTR station: 91M bus (use Exit B2); 11 minibus (use Exit B1)
From Po Lam MTR station: 91M bus (use Exit A2); 12 minibus (use Exit B1)
From Ngau Tau Kok MTR station: 104 minibus (use Exit A)