You have two options;
1- The Public /State Universities
2- Private Universities
First of all, you have to know that there is an exam (YÖS)
It is not a general exam, each university does that themself.
Some of them don’t do this exam and accept students with high school diplomas.
Mainly, private universities do the exam to give a discount.
But if you want to be a student in public/state university you have to get good points as a result of the exam/good marks.
After that, you can apply to universities to get an acceptance letter. Some universities give a pre-acceptance letter. (Its works as same acceptance letter)
You can get a student visa with the pre-acceptance letter. However, you need original acceptance letter to register.