There are many ways to keep track of your assignments that are due. You can:

View the Recent Activity feed on your Dashboard.
View the To-Do List on the right sidebar.
View the Coming-Up feed on the right sidebar.
View your Calendar.
Hover over the Assignments link in the Global Navigation, and view the To Turn-In list.
Locate and click on the Assignments navigation link, and view the Upcoming Assignments list.
Locate and click on the Grades navigation link, select the appropriate course, and view your Assignments list with corresponding grades.