You will find that teaching styles in the US are much different than those in other countries. Teaching in the US is more interactive and less dependent on rote memorization. Students regularly interrupt faculty to ask questions or offer constructive criticism of part of the lecture. This is encouraged, since professors prefer discussion and debate to passive silence. You will also notice that the students and faculty tend to dress rather informally. Faculty will have open office hours for students to come by and ask questions.
Class sizes tend to be smaller in the US than in other countries. Although first-year students may have a few large classes, most classes are small, with 15 to 45 students. The large lectures will often have small recitation sections run by teaching assistants or faculty. Recitation sections review the material presented in the main lecture, supplement it with additional material, and provide an opportunity to ask questions.
Your grade in most classes will be based on your scores on tests, quizzes, and assignments. If the class has a recitation or discussion section, active participation can improve your grade. The better the professor and teaching assistants know you and your work, the better they will be able to assess your progress.
Unless the professor has indicated that collaboration is expected, you should do all of the work on your own. Collaborating with fellow students on individual assignments is considered cheating. Studying with others is ok, but assignments should be completed individually. Likewise, quoting a text word for word without properly attributing the source is plagiarism. Cheating and plagiarism is grounds for failing a class or even expulsion from school.