From the airport
Train: Take the train S2 to get to Bahnhof Neustadt. Change to the S3 and alight at Pirnaischen Platz. From there, the hotel is a 5 minute walk. It's a 35 minute trip in total.
You can choose between a single ticket (2,30€), a day ticket (6,00€) or a ticket for a week (21,00€). Within the ticket price, you can take both the train and the bus.
Taxi: It is a 20 minutes trip, depending on traffic, and costs around 40€.