View the screencast or skip the video and read on:
A Moodle assignment activity is where your instructor records your grade and provides feedback on your work. Sometimes a Moodle assignment activity is just to remind you about an assignment that is submitted in person, and for these assignments the feedback may or may not be received through the Moodle assignment activity.
To find your assignments you can either browse the course for the assignment icon 
or you can navigate to the Activities block on the right side of the course and click on Assignments to see a list of all assignments in the course.
This list of assignments displays what unit the assignment is in, the assignment name, due date, submission status, and, if it has been graded, the assignment grade. To see the assignment description, click on the assignment name.
To submit your assignment, navigate to the assignment activity and click the Add submission button.
You will either make a File submission, such as a Word document, or type text into the Online text submission area. The assignment description will usually indicate what is required, but file submissions are much more common. To upload a file, simply drag and drop the file into the File submission area. Alternatively, you can click on the Add new file button, click Choose File, navigate to the file and select it, click the Open button, and click the Upload this file button.
If it's an online text submission enter the text into the Online text submission box.
Once you have finished either uploading a file or adding online text, click the Save changes button.
Depending on the assignment settings, you may be able to edit your submission. Note that clicking the Save changes button updates the date and time stamp for the submission, so only click this button if you are either making your original submission or are making changes to your submission. Clicking the Save changes button after an assignment's due date, whether or not you changed anything, will make the assignment appear late.