How do I take public bus or MTR from HKIA to Tsim ShaTsui and my hostel is at Mirador Mansion?

Bus octopus card from any 7-11 or ticket booth at any MTR station . Octopus card are very convenient way of mode of pay ment.
The MTR is very easy to learn and they are color coded. First find your Origination point and your final destination. Looking at he color coded map you can trace what color train and also the name of the train always the same with the last station destination of the route.

Buy Octopus card at MTR station.
From the Airport take MTR South Hong Kong Line. Get off at Kwai Fong transfer to Red line Admiralty way line and get off at Tsim Sha Tsui.

The bus is much cheaper and if your in no Hurry, $33 HKD will bring you at Tsim Tsa Tsui compared to more than a $100 HKD on a one way train. Travel time by bus is normally 45 mins. If your arriving by day time Take the bus Cityflier Bus A21 at the bus terminal outside the airport and get off at the 14th bus stop Middle Road , Nathan St Mirador Mansion is just across the street.