From the Gradebook
To look at a particular student's activity in the course as a whole, first click on the student in question in the Gradebook (in this case, "Brown, Betty").
From the screen below, you can see the particular student's Score and date Submitted for every assignment in the course (if there is no score/date submitted, then the student has not completed the assignment).
From the screen above, you can drill into each of the particular student's assignments, you can change grades/due dates for the student, and you can look at the student's complete activity breakdown by minutes. To look at the complete activity of the student by minutes, click the icon at the top right of your screen.
From the screen below, you can see exactly when the student in question Started each assignment (if the student started it) and exactly how much time he/she spent completing the assignment. You can also see the Total time spent on all assignments for the student.