Yes.
You definitely have to apply for admission into private universities or colleges seperately. Application forms will be available in the official website of each college or universities. You can register yourself in the official website and complete the application form using your personal details. After completing the application form you will be called for admission if you are selected.
Currently, all private universities in the state have their own entrance exam. The exams are usually held on an all-India basis soon after II PU/class 12 exams. With students forced to take multiple entrance tests paying huge fees, there is a demand for single entrance test for all private universities.
But students can get direct admission also.
All the best