Adding an Assignment
The "New Assignment" link can be found on your home page, or any course page.

Just type your assignment name in the "Assignment Name" field and select which course it's in using the drop-down menu.
Select the due date of your assignment by clicking on the day on the calendar. You can now click the "Add Assignment" button and your assignment will be added. However, if you want to explore the sharing and notification options, read on.
The Sharing Options

Right underneath the calendar is a link that says "Show sharing options" which displays a list of all your partners (if any). You are able to allow selected partners to see your assignment on their home page.
Read more about sharing with partners.
The Notification Options

These options let you specify if you'd like to be notified a certain time before the assignment's due date.
Read more about notifications.