Hello Curlysil
As an US citizen who has been lawfully declaring

(and paying where applicable) taxes to both the US and CH for the past 5 years, this is what I can tell you from my own personal experience.
1- There is a tax agreement between CH and US, where you pay taxes to CH first (country where you are working), but once you pass the maximum allowed threshold (I think it is 80-85K USD but please do not quote me on this one), you start paying to the US on the difference above the threshold. For example, if you make 100K USD salary in CH, you tay taxes in CH, but you will also be taxable for 15-20K in the US.
2- Uncle Sam "requires" you to file taxes every year even if you do not meet this 80K threshold
3- I own property in the US that is currently rented out, so I must file taxes every year.
4- I have used a tax advisor for the past few years due to my complicated personal situation, and tax advisors can find everything that could posible be deductible, such as my CH rent, my US storage fees etc etc from the amount I have to file in the US.
Hope this helps, and here is the link of the lady I have used in the past
www.ustax.ch
If you have any more specific questions, please feel free to PM me
cheers
laifu