There are numerous views and screens available of the Moodle gradebook, but only a few are commonly used.
When you first access the Gradebook by clicking on “Grades” under the Navigation box, the Grader Report view is shown as the default. This view shows all the grades for all the students in the course, with scrollbars along the right side and bottom for classes with a large number of students and/or assignments. To sort the students by a grade column, click on the arrow symbol next to the column name. This will allow you to toggle between ascending and descending views of the grade column.
To modify grades within this view, click on the “Turn editing on” button in the upper right. Note that this just allows editing of the gradebook, and is not the same as the course edit button. After editing is turned on, an edit icon (wrench) is shown next to each grade. Clicking on that will pull up a data entry screen for the assignment. Alternatively, you can enter in a new numerical score in the box, and then click “Update” at the bottom of the page for the change to be saved.