If you are from a third country (non EU/EFTA) you will need a permit to work in Switzerland. Only your future employer can apply for this permit and the requirements for a successful application vary per canton. In addition to professional skills some other criteria like language skills and housing situation will also be taken in account by decision makers.
General information on the Swiss labor market for non EU/EFTA nationals can be found on the website of the State Secretariat for Migration SEM. On this site you can learn more about the basics of the admission to the Swiss labor market as well as on the procedure.
On the website of Swissuniversities, you can find a summary of the work permit regulations that apply to students specifically. Read also the pdf under "Overview" at the end of the website.
Since the requirements vary in each canton, you can find here all the information on your opportunities in the Canton of Zurich for a part-time job during your studies and for (mandatory) internships as well as more information on work permits after your graduation.
IMPORTANT: Please note that we have linked to the page of the Office of Economics and Labor (Amt für Wirtschaft und Arbeit - AWA) because this page is very clear and covers most questions.
However, the AWA is only responsible for employer inquiries.
If you as a (potential) employee have any questions that are not answered above, please contact the migration authority of the canton you would like to work in.
An overview of all migration offices in Switzerland can be found here.
We from the Career Services support you in collaboration with the ETH Career Center twice a year with an event called «Working in Switzerland», which you find in our events calendar.