Click on the assignment to enter it and you will see a details page for the assignment. This page tells you; the submission status, the grading status, how many attempts/submissions you have made and the due date for the assignment.
To start the submission process, click on 'Add submission'
Most assignments will be of a file upload type, you will see the following screen (if your assignment allows pasting of text, you will see a text editor into which you can paste your text)
Please note, the file submission window shows you how many attachments are allowed, and what the maximum file upload size is.
Tick the checkbox to accept the submission statement 'This assignment is my own work, except where I have acknowledged the use of works of other people.' For group assignments, the statement will vary slightly.
You can either drag and drop your file on to the upload window, or you can use the 'add file' icon, 'Upload a file' link , and then button, to manually browse for and upload your file.
The details page now shows your new submission status and a link to the file you uploaded. You also have the option to Edit your submission or remove a submission.
If your instructor has enabled Turnitin within your Moodle Assignment, you will see a link to your Turnitin Similarity Report and your Submission ID under File submissions.