Don't go to that hotel. It is not in Zurich, it's in a village right out of Zurich and it's more a motel next to the motorway that goes towards Austria. Change that booking immediately and find one in the city of Zurich. Try booking.com or go to this website
http://www.zuerich.com/de/page.cfm/Diver… You've chosen the wrong Ibis. Take the City-West Ibis and you're in the middle of everything and all your questions above will be solved.
As for the transportation from the airport: That is easy. Either take the train to Zurich City. It runs every 5 - 10 min. There are either ticket counters or self-service ticketing. Everything is marked very clearly. You can't go wrong when you come out at arrival. It's pretty small there.
You can also take the street car no. 10. The ticket machine is at the station which is just in front of the terminal. Just follow the signs at arrival. For the street car, you'll have to down- and upstairs on escalators but everything is very easy to find. You'll be ok.
JUST CHANGE THAT HOTEL IMMEDIATELY or you'll be lost in space. Here's the address of the IBIS City-West to which you should change:
Hotel ibis Zurich City-West, Schiffbaustrasse 1, 8005 Zurich, Tel. +41 44 276 21 00
Lived and worked in Zurich for 6 months.