There are two ways of looking at student activity on an assignment. The first way is to look at overall student activity on the assignment. The second way is to look at one particular student's activity on the assignment. The first method is the macro level, while the second is the micro level.
Looking at overall student activity on an assignment
From your home page, click Gradebook.
From within the gradebook
Click on the assignment you would like more information on (in this case "Exercise: Sentence fragments 1").
From the assignment
Once within the assignment, you can scroll down to access all of the overall student metrics for the assignment. You can see the Frequency of Scores, Frequency of Grades, Submissions, and Question Difficulty/Discrimination.
Looking at one particular student's activity on an assignment
From within the Gradebook, click on the assignment in question (in this case "Exercise: Sentence fragments 1").
You can then see this particular student's responses to each of the questions in the assignment. From this screen, you can also alter a student's Score on the assignment, provide Feedback to the student or yourself, and Excuse the student from the assignment (an excuse puts an "X" in place of a grade).