There are two different ways to consult the people, depending on the nature of the issue: the popular initiative, and the referendum.
Popular initiative
Any Swiss citizen has the right to propose new legislation by launching an initiative - although normally initiatives come from pressure groups rather than individuals. If they manage to gather 100,000 signatures in support of the proposal, it must be put to a nationwide vote.
In theory, an initiative can only deal with constitutional matters, but in practice they have been held on a variety of issues.
Initiatives have been held recently on matters such as cutting military spending (rejected) and limiting the foreign population to 18% (rejected).
More "exotic" initiatives have included making it easier to open casinos (accepted), protecting marshland (accepted) and banning the production and sale of absinthe (accepted). The first initiative under the current system, put to the vote in 1893, called for a ban on the Jewish method of slaughtering of animals without stunning them first. It was accepted, against the advice of parliament.
Referendum
The Swiss use the term "referendum" for a popular vote called to challenge a piece of legislation already approved by the Federal Assembly. If any person or group opposed to the new law manages to collect 50,000 signatures within 100 days of the official publication of the proposed legislation, the voters as a whole are given the chance to decide.
In most cases, a referendum is only called if those who feel strongly about the issue manage to collect enough signatures.
However, the authorities are obliged to hold a referendum if the legislation involves an amendment to the constitution initiated by the government, or any proposal for Switzerland to sign a major international agreement which cannot be rescinded.
In the case of an initiative or a mandatory referendum, there has to be a "double majority" for it to pass, meaning a majority of the people as a whole, and a majority of the cantons must approve it.