The train is your best bet. When you arrive in the airport you will see signs for the train (no need to speak German, they will have a small picture of a train on it).

One floor above the actual train tracks there are kiosks and desks where you can buy your ticket. For me, its easier to wait in the line (takes no more than 5-10min) and buy the ticket since they can tell you the track number. The
people at the ticket boths speak english (at least everyone I've met).

Airport to Hotel in the taxi is very expensive for how far it is away. $40-$80 one way.

I'm usually in/out in one day (over night transit) so I buy a 24hr pass.

Once arriving in downtown, you can walk from the train station to the hotel if you don't have a lot of luggage. Its about 10-15 min - a nice walk. Or you can take the tram which drops you off within a couple hundred feet of the hotel. Other option is a taxi but they are expensive even for this short trip (~$16). I'll update this post with the tram numbers to take for the hotel tomorrow when I return home.