If your school-leaving certificate is not sufficient for university admission, you will have to take an additional University Entrance Examination (sometimes also known as "University Entrance Assessment Examination", or German: "Feststellungsprüfung"). You will be tested on your knowledge of the German language as well as subject-specific knowledge relevant for your desired field of study. Once you pass the examination, you will earn the qualification for subject-restricted study.
Most applicants prepare for this examination in a two-semester foundation course (German: "Studienkolleg"). In Lower Saxony, these courses are offered by Niedersächsisches Studienkolleg. Since places in the foundation course are high in demand, you will have to take an entry exam. Only the best candidates in this test will be offered a place in the foundation course. Excellent preparation for the entry exam is therefore crucial.
You can also take the university entrance examination as an "external applicant", without attending courses at Studienkolleg first. This, however, is not recommended due to low pass rates among external exam candidates.
You will find further information regarding the qualification assessment examination and Niedersächsisches Studienkolleg here.