There is a lot of mystery on how can a foreigner get a weapon purchase permit, and it varies from canton to canton. My experience comes from Schwyz, but I think the general concept is more or less the same at other places as well. Before we continue, the following tips apply if you own an L or B permit. C permit owners don't need to do anything special, just apply for the weapons purchase permit (WPP from now on) at the Waffensprengstoff division of the cantonal police. The most important requirement, and this applies even if you have a C permit, is that you must not come from the following list of countries: Croatia, Bosnia-Hercegowina, Macedonia, Tukrey, Sri Lanka, Algeria or Albania. This looks like blatant discrimination, but unfortunately this is what is in the law.
Satisfying the first condition, the next thing you need is a proof that the authorities in your home country have nothing against you purchasing and owning guns in Switzerland. In most countries, the police will give you this document, sometimes the ministry of internal affairs. Some countries do not issue a document like that at all (Germany for example), which means that you won't be able to get a WPP until you get a C permit. In my case, I just went to the police and told them that I need proof that "They have nothing against me owning firearms in Switzerland".
Having said document, you need to translate it to german and have it stamped at your consulate, proving the authenticity of the german translation. Many consulates offer translation services as well (for a fee), where they can give you an official translation on spot. This might save you some time having to run around and hunt for translators.
The next thing is then to go to the Waffensprengstoff division of your kantonal police and lodge the request. They should send you the WPP within a week. There is usually a limit on how many weapons you can purchase, e.g. 2 rifles and a handgun.
If you have problems, the best thing is to become a member of ProTELL ( www.protell.ch ). They speak english and can generally help you out with the process and explain the rules. They also actively support the free weapon owning right in switzerland, which I think is a very good cause. Membership fee is 40 CHF a year, which is not that bad considering the ammunition prices in Switzerland