As an American living in Switzerland, you are not only taxed in Switzerland but taxes are due in the US as well. The United States is the only country in the world (other than Eritrea) to tax their non-resident citizens and green card holders on their nationality and the right to be resident in the US no matter where they are living at the time.
The Swiss Confederation and the US have signed a convention for the avoidance of double taxation concerning taxes on income.
The Double Taxation Agreement between Switzerland and the US aims to prevent the same income from being taxed in both countries equally. There are, however, some aspects that cannot be avoided, and it generally results in a person paying the higher tax of the two. In every case, US citizens must complete a Swiss AND a US tax return.
To get things right, right from the beginning a tax expert should be consulted.