On foot
The main train station, old town and the lake promenade and all nearby tourist attractions are easily walkable. You may find that you don't need transport for most of your tourist needs once you get into the city.
By bike
You can "rent" bikes, skateboards etc. for free from 7AM-9:20PM daily May-Oct at several places in Zurich and year-round at the central train station. All you need is your passport and a CHF 20 deposit as guarantee. This offer is called "Züri rollt German only" (http://www.zuerirollt.ch). You can get and return the bikes at several locations: the bikegate just next to the central station, next to the "Globus City" shopping centre, next to the opera, or at the Swissotel in Oerlikon. If you can't find these places, don't hesitate to ask some locals, they should know at least the bikegate at the central station. The Zurich Transit Company, VBZ also provides information about these bikes in English (http://www.vbz.ch/vbz_ope...). Nevertheless, you shouldn't count on it because sometimes the "rent" spots run out of bikes.
By public transport
Zürich is famous for its highly efficient, clean and safe public transport system, owned and managed by the Zürcher Verkehrsverbund ZVV which covers the entire canton of Zürich as well as Rapperswil-Jona in the canton of St. Gallen and Pfäffikon SZ in the canton of Schwyz. The network includes trams, buses, S-Bahn suburban trains, cable cars and boats. The size and complexity of the network may be daunting at first, but you will soon realize that there are dozens of ways to get from one place to another and following any of them will still be efficient.
The system is divided into numerous fare zones, with the city centre and innermost suburbs being in zone 10 and the outer suburbs located in other zones Winterthur is in zone 20, for example, and the more zones you pass through, the more you'll have to pay for your journey. There are single tickets, day cards, monthly cards and annual cards. The monthly and annual cards are collectively referred to as ZVV NetzPass.
Tickets must be purchased from a ticket vending machine before boarding or from one of the ticket selling kiosks. The ticket vending machines are in German, English, French and Italian and offer almost all regular tickets available not personal tickets though. You select the zones you wish to pass through upon buying the ticket, with a zone map on every machine as well as clear instructions coming to your aid, so feel free to choose! Once you've got your ticket it gives you access to all modes of transport.
If you're staying for a longer period, consider a monthly ZVV NetzPass, because even though there are no regular tickets valid for something between 1 day and a month, it takes only 10 zone 10 day cards for a zone 10 monthly card to be cheaper. When travelling in all zones, it takes only 8 day cards for the monthly card to be cheaper.
If you don't mind starting your travels after 9:00, the "ZVV-9-UhrPass" is the best option. It is available as both daily, monthly and annual cards and will save you a lot of money compared to regular similarities, especially given that the 9:00 rule does not apply on weekends.
There are also so-called Z-passes, which can be used not only in Zürich, but also in one of the neighbouring cantons Aargau, Schaffhausen, Schwyz, Zug, St. Gallen or Thurgau; however, only one additional canton is possible, so if you're not going to one neighbouring canton more often than the others you are probably better off with just a normal all zones Zürich monthly card and buying single ticket from the last valid station to your final destination. The Z-pass system also has its zones, even in the neighbouring cantons. It is only available as monthly and annual cards and can not be bought from ticket vending machines.
For all details regarding fares, see (http://www.zvv.ch) in German or (http://www.zvv.ch/en) in English
The Swiss Pass is valid on all public transportation in Zurich, and if you are a tourist visiting most of Switzerland, this may be your best way to saving both money and time spent trying to figure out zones, routes, and fare options. Eurail passes are valid only on the S-Bahn and boats. Interrail passes are valid on the S-Bahn although the ZVV website claims a "reduction" for other routes for Interrail holders. Nevertheless, you may find you don't need the trams and buses if you don't mind walking around a little.