The Finnish higher education is divided to two branches. The actual universities offer Bachelor’s, Master’s and PhD programs in all fields. Universities of applied sciences offer more practical studies and only Bachelor’s degrees in specified fields like nursing, engineering, arts like dance, and media production.

Flow chart of the Finnish school system. No tuition required at any step.
Students who opted out of high school and went to vocational school can apply to both as long as they meet the requirements. Usually they go to the applied sciences institution first and then apply to university. High school is a faster track to university, but students also go to the applied sciences institutes from there. I really appreciate the flexibility of the system. You are never shut out from higher education.
Students apply directly to the department, to a certain major. Your school grades are taken into account as well as the matriculation exam (high school students), and the main requirement is the entrance exam specific to the major. Each entrance exam can be based on one or more books and contains application of the learned material to answer problems. For applied sciences, entrance exam is based on high school courses, but some fields like nursing might require psychological testing as well as group interaction tests.

Universities in Finland. Modified from http://www.isep.org.
There are no core courses required in the university. Only compulsory non-major classes are language classes (English and Swedish). All the general knowledge classes are taken at high school level. Minors can be used to widen one’s education. For example marketing, biology, chemistry, and microbiology are popular minors for biochemistry major. In retrospect, maybe having some sort of common core could have been beneficial and allowed introduction to more varied minor choices. Students have the freedom to not show up in most classes as long as they acquire the information on their own, return any homework required, and pass the exams. This is expected to change as teaching methods are developed to more student centered.
All higher education in Finland is tuition free at the moment. Administrative fees (includes student health care and dental fee) are low, around 90 euros ($125) per year in my old university. For citizens of Finland there is an automatic stipend to cover living expenses and support for renting an apartment as we have no dorms. Most students avoid loans like they are the plaque. The meals on campus have student discount pricing and consist of quite healthy home cooked style fare (side salad, bread, warm main, milk or water). Students take care of buying their books when needed, but libraries commonly carry enough books for most students to use during the semester. I bought around 6 books during undergrad.

Student housing (www.psoas.fi) and student life at University of Oulu
Recently we have started several master’s programs completely taught in English. For example at the University of Oulu master’s degrees offered in English are from Business and economic, Education, Engineering and architecture, Health sciences, and Natural sciences. These have attracted students from Europe, Africa, and Asia.
The higher education system is flexible in Finland and students financed well by the government. It is not a perfect system by any means and faces many of the same problems as other higher education systems in Europe and US. Keeping the higher education available for all qualified students is still a priority and is seen as a way to enhance equality. As Finland is a small country with limited natural resources, our economy depends on highly skilled people.