Switzerland is hard even for EU citizens to work in. My friend is British and wants to work there. She can't. So she's looking into living in France on the border and spending the weekends in Switzerland.
2. International Schools
You can try to get a job at an intl school in one of the countries near Switzerland. If you're interested in working in the EU and spending the weekends in Switzerland, see EU for non-EU passport holders for more info.
3. Investor and Self-employment Visas in Switzerland
offers an investor visa for those from non-EU countries. Those from EU countries can get a self-employment visa or an independent visa.
4. Fellowships in Switzerland
There are legal ways to work in the EU and Switzerland through fellowships and teaching exchanges. DECS is one of the organisations that places teachers in Switzerland, as well as Denmark, France, Germany, and the UK.
5. Au Pair, Nanny, and Governess Jobs
Au Pairs are usually under the age of 30 and don't have formal childcare qualifications. Nannies do have formal qualifications. Governesses usually teach the children as well as care for them. You can find a list of programmes here, WHV and short term jobs.
6. Marriage
If you get married, you can legally live there.
7. Study
If you study in Switzerland, you may be able to work part-time and then find a job in Switzerland after graduation. You could even study a foreign language like French of German.
8. More info about the EU and Switzerland
You can find lots of info Europe for non-Europeans. Read through it all and then look at the bottom. There are country specific programmes. The Ministries of Education of France and Spain have programmes that place Asst English teachers around those countries. You won't make much, about 700 euros a month, which is about $1000, but you'll be in Europe legally and could easily fly to Switzerland on airlines such as Easy Jet and Ryan Air.
9. Move to a different country
Many times it's easier to live in a third country. I lived in my husband's for 6 years, now we live in Korea. We're both foreigners and it's much easier that way.
Conclusion
Switzerland has been an oasis for many years and because of that it's harder to live in legally than other countries. However, nothing is impossible. With a bit of luck, hard work, and research you should be able to go there.