At Kloten Airport, there is a Swiss Rail (SBB) station under the terminal buildings. You can take the train directly to the Zurich Hauptbahnhof, the main station, sort of like Grand Central. Go second class as it’s a very brief ride.
From there,I would walk down the main street, the Bahnhofstrasse, to the Paradeplatz, and then to the lake.
Here is a listing of different tours (in English) from the city website:
http://www.zuerich.com/en/page.cfm/excursions/individuals/zuerich_city/zuerich_city_x
If you are looking to buy any grocery products, there is a Co-Op supermarket near the train station and along the Bahnhofstrasse several department stores like Jelmoli and Globus have food departments.
Please note that in my experience you will very often see Swiss products that are exported to the United States with a hechscher (e.g. certain chocolates) sold without a hechscher. (In Europe, many products have no MARKED hechsher but are known in the Jewish community as being kosher.) Discuss with your rav whether or not you should buy them.