When you use Moodle's quiz tool a lot of the question types are automatically graded for you. ( Multiple choice, true & false, matching )
However, you may want to use Short Answer or Essay questions in your exam which will have to be graded manually.
To manually grade these questions you must first click on your exam on your main course page.
From here, you will see how many student attempts have been made on your exam. Click on the number of attempts.
This will show you each students individual attempt. You may have a mix of automatically graded questions and questions that require manual grading. Scroll over to the questions that require grading. Find the question and student you want to grade and click on 'Requires Grading'.
This will open up the individual question. Click on 'Make comment or override mark'.
You will now see the student's response and can include a comment as well as provide a mark.
Once you are done, hit Save at the bottom.