I can't speak for Finland, but here in Germany, you need Hochschulreife (university entrance qualification) to attend a university. There are two basic ways to get there, depending on which type of secondary schooling you attended.
After typically attending primary school for four years [1] (age 6-10 or 7-11), there are three basic types of secondary schools:
- The Hauptschule (general school) is five years long (for a total of nine years). This level of education traditionally [1] prepares for vocational training in the crafts, e.g. in construction or as a barber and so on. As far as I know, there is no way to get to university from here.
- The Realschule (real school) is six years long (for a total of ten years). This level of education is traditionally [1] required for office staff. From this point, you can get to the Allgemeine Hochschulreife by completing vocational education in a profession of your choosing (typically 3 years), then attending school again for 1-2 years, which gives you the Fachhochschulreife (entrance qualification for universities of applied sciences).
This is how my brothers got their degrees: They both went through Realschule, completed vocational training (one as a road builder, the other as a gauger), then got the Fachhochschulreife, applied to a university of applied sciences, and completed a 4-year curriculum to become certified civil engineers.
- The Gymnasium is eight or nine years long (for a total of 12-13 years). Successful completion gives you the Allgemeine Hochschulreife (general university entrance qualification) which allows you to enroll at any university in Germany.
This is how I did it. The only barrier that might exist is a Numerus Clausus: If courses are in higher demand than what universities can muster, they can restrict entry to students with a grade higher than a certain threshold. (The grade is the one on the entrance qualification.)
In my case (I studied physics and computer science in Dresden), this didn't apply: All I had to do was to fill out a form with my name, address and desired major and hand it in before a certain deadline. Also, there is a small tuition fee of around 250 euros per semester. Of this, about 180 euros pay for my subsidized public transit ticket. About 60 euros go to the Studentenwerk (student services), which operates the university's canteens and offers counseling. The remaining change goes to the student's council.
[1] The fine print for all of these descriptions: The education system is in constant upheaval in Germany. Every politician or focus group has their own opinion on how the system should be. Therefore, there's not just 3 forms of secondary school. More like 30 or 40 (over all 16 member states of the Federal Republic of Germany). Secondly, there's a similar trend in Germany than in the US or elsewhere to put less and less value on the shorter tiers of secondary school. More and more roles that used to be Realschule plus vocational education now require a degree. And more and more vocational trainings that used to require Hauptschule now require Realschule. Whereas, a few decades ago, maybe 10% of pupils attended Gymnasium (and went on to university), nowadays it's more like 50-60%.