Log in as a Brightspace student.
Select the course that you'd like to download Submissions from.
From the top-right of the course page, click on your Profile then select Progress.
From the list of indices on the left-side panel, select the Assignments option.
From the list of assignments, scroll to the assignment of your choice and click on Details.
Under the Submissions section click on the Hyperlink with the file name (usually the name of the file while you submit assignments eg: Assignment2.zip).
From the next window select the location to save the file on your computer and click on Save.
Repeat step-5 to step-7 in order to download submissions of your choice OR all submissions of yours in the respective course.