Recent submissions will appear as notifications (the bell icon) in the top right corner of your dashboard. When you get a new notification, you will see a red dot with the number of recent submissions on top of the bell.
Click on the bell to see a list of the recent submissions, and click on the notification you would like to view.
Alternatively, click on the class for which you would like to view submissions within your 'Classes' tab.
Click the "Assignments" tab under your class name.
Here you will see a list of the assignments you have given to this class, and under the 'Submissions' column, you will see the number of submissions which students have handed in for grading. Click on the little blue arrow next to the number of each student's submissions to see which submissions they made.
By clicking on the 'Students' tab in a class, you can see a list of all of the students in the class and all of their submissions, which will appear under the 'Submissions' column.