You got into graduate school at a great university! Hooray!
You should be proud. But now you are worried…
Universities in the US/UK/Australia/Canada do things differently than in your home country.
Now you are thinking:
Oh my God, I’m going to flunk my exams and fail my courses…
Yes, things are different. There are unwritten rules that all students must know.
How do you study for exams at a UK or US University?
I have studied at both US and UK universities, and taught at a university in Brazil. What professors expect of students in an English-speaking country is very different from some other countries, so I wanted to give you some tips.
Tip 1: Read the Syllabus (Course Description)
The syllabus usually tells you what material the professor expects you to master during the course. It might provide details like which topic will be covered each week or even each class. It almost always lists recommended references or textbooks.
Tip 2: Read a textbook

Sometimes a professor follows a textbook closely and will tell you which textbook section corresponds to each lecture. I always did this when teaching! I think this is extremely helpful for students, especially because some students might like to read the textbook BEFORE the lecture.
If English is not your native language, at least skim the textbook before the lecture to learn the new keywords for that topic in advance.
In the US/UK, the lecturer assumes that you are reading a textbook. In the live lectures, she or he is acting like a tour guide, showing you what is important by talking about it. But you need to learn more by reading a textbook.
If the syllabus lists more than one textbook, maybe each one covers part of the syllabus. Or maybe they all cover the same material but with a slightly different approach. See if you can check them out of the library and try to map each item in the syllabus to a section in each recommended textbook. That way, if you do not understand the explanation in class, you know where to look in the textbook(s) for clarification.
Back when I was in law school in the UK, the lecturers always suggested more than one textbook for each course, covering the same material. It was kind of like Russian Roulette: just pick a book and hope it is good. One year, the textbook I bought for a course was just HORRIBLE! I really hated it.
So, after about a month I bought the other textbook and it made such a big difference. I really liked the second textbook, reading it was a pleasure and I no longer had any problems studying for that course.

Tip 3: Prepare for exams by answering questions

If your exam will have problems you have to solve (math, science, engineering), prepare for it by answering questions. Preferably under exam conditions (no notes/books if the exam will be closed-book). Many textbooks will provide answers to some problems in an appendix at the back of the book. Do those problems first! If not, then do the example problems (without looking at the worked-out examples) in another, similar textbook.
If you will have to write essays on the exam (social sciences, humanities), prepare for it by writing essays.
Whatever the type of class, prepare for the exam by doing whatever it is that you will need to do on the exam. Do NOT just re-read your notes! That is the worst possible thing you can do. A big waste of time.
Tip 4: Keep track of the things you get wrong, and test yourself on them again before the exam

Everyone has done this… you try to solve a problem, but get it wrong. You look at the solution and think “wow, that was not so hard, now I understand!” But, 50% of the time, if you try to solve that same problem 2 weeks later, right before the exam, you will get it wrong again.
So, keep track of the problems you get wrong on a special page in your notes, and try them again (no peeking!) right before the exam. This will really test your understanding of the things you found most confusing.
Good luck!