Assigning is available from any story in LitLab or directly from your Dashboard.
Before assigning, make sure your students are rostered. You can roster using any method below:
Open any story in the LitLab Library.
Click Assign in the upper-right corner.
The Assignment window will appear.

Go to your Dashboard.
Click + New Assignment.
The same Assignment window will appear.

Whether you start from a story or from the Dashboard, the steps are the same: