Table of contents
Grading a Moodle Assignment 
You can click on the assignment from the course page or you can click on the assignment in the "Grader report" page in Grade book.
Scroll across the graded items till you find the item you want to grade and click on the assignment name.
This takes you to a Grading summary page (if it does not more than likely your role is not set to a role that allows grading)
This page will tell you how many participants, how many have submitted and how many need to be graded. When you are ready to grade the assignments clicking "Grade" will take you through each users 1 by 1 however "view all submissions" will allow you to choose the assignments to grade
From this page you can see all student who have submissions, download submitted documents, enter feedback comments, and record grades. You can perform all of this from this page, but we will look at the individual student view. Note under "Status" this should read "Submitted for Grading, " however if a student uploads a document but neglects to click on submit, this can read "Draft"
To view the individual grading area click on "Grade"
On this page you can download the student submission by clicking on it's title (1), enter the grade (2), leave feedback (3), and upload supporting grading document such as a gradebook, grading worksheet or marked-up document (4).
When you are ready Click "Save Changes"
Entering Grade Manually (for overriding previously graded items or for manually entered grade items) 
If you have an assignment that is submitted outside of Moodle and you entered a graded item for it in gradebook, or if you want to override a graded item you can do this from gradebook.
From the Gradebook main screen. Ensure you have the "View Tab" selected and the "Grader report" sub tab selected.
Use the scroll bar at the bottom of the page to scroll across to the Assignment you want to manually enter.
When you find the assignment you want to enter, just click on the cell for that Student.
Enter the grade, then hit enter.