The Assignment activity in Moodle has a unique feature that allows for advanced grading through criteria-based assessment or Rubric. In order to activate and use this feature as you create an assignment, select Rubric under the pull-down menu in Grade block in Assignment settings:
and then click Save and display button at the bottom:
Moodle will take you to the page with Advanced grading options where you will be able to either create a new rubric from scratch or use an existing one as a template:
NOTE: You can also activate the Rubric and access this screen from the pre-existing assignment by clicking on that assignment and then selecting Advanced grading from the Gray Administration Gear in the upper right corner: