Switzerland is a surprisingly good place for cycling, largely due to its good cycling network. Swiss bike efforts are often stylized under the heading "Veloland Schweiz" which is Swiss standard German for "bike country Switzerland".
Rules and laws
According to Swiss traffic law, a bicycle is considered as a road vehicle, therefore it is prohibited to cycle on sidewalks and foot paths, except for when explicitely indicated otherwise! As a bicycler you have to follow the same rules, and rights, as any other traffic member, such as cars and lorries. Therefore make sure you know the extensive Swiss traffic rules and traffic signs.
Cross country mountain biking is a huge sport in Switzerland. This is unsurprising to anyone who has watched a world cup race before and seen half of the top ten seized by Swiss riders. The main reason for Swiss excellence in the sport is probably the amazing training area they have in their backyard. Thus Switzerland is an amazing place for everyone who likes mountain biking. To find routes, you can use the Swiss Singletrail Maps and veloland.ch. These cover the whole country in the scale 1:50,000 with single trails and routes mapped and classified. You have to buy them in paper since they’re not available online.
The cycling infrastructure for everyday cycling varies between the cities. Basel, Winterthur and Berne are the champions which can almost compete with Dutch and Danish cities. In general the German-speaking regions are better for cycling than the French-speaking ones. There are many Swiss cities where you can rent bicycles if that is your means of traveling and you can even rent electric bicycles. During the summer it is quite common for cities to offer bicycle 'rental' for free!