There are three types of higher education institutions in Switzerland.
Students who go to a university or a federal institute of technology learn the scientific basis of their area of study. There are two federal institutes of technology: the Federal Institute of Technology in Zurich (ETH Zurich) and the Federal Institute of Technology in Lausanne (EPFL). An academic baccalaureate from a baccalaureate school provides direct access to university.
Students who go to a university of applied sciences acquire practice- and application-based knowledge. A federal vocational baccalaureate or a specialised baccalaureate provides direct access to a university of applied sciences.
Universities of teacher education and training train teaching staff.
You can apply directly to a higher education institution. The website of the umbrella organisation of the Swiss universities provides the contact information of the higher education institutions (web page available in German, French and Italian) and the application deadlines for study programmes.
Most programmes do not have an enrolment limit. Exceptions exist in particular for the fields of medicine (access to the programme requires student to have passed an aptitude test), chiropractic and sport and physical education.
Universities of applied sciences also have enrolment limits in certain fields of study. Contact the university you are interested in for more detailed information.