Start by clicking on your class on the overview page (this is the first page you come to after logging in).
Assignments that are open for submission will have a green Submit button next to it. Click Submit and a new page will load.
On this page, upload your file or enter the text on the page (this will depend on which type of file your teacher allows).
Click the green Submit button at the bottom.
You'll be shown a preview of the assignment you have just submitted. If your email notifications are turned on you will also receive an email confirming your submission.