The instructions below are also available in this video tutorial.
On your profile page, locate the project you want to use as a template for the assignment and click the three dots to open up the project dropdown menu (1). Choose "Create assignment" (2) to open up the Create assignment dialog window (3). (There's also an assignment button next to the download button.) At the bottom, click the Google Classroom icon (4). This takes you to Google Classroom. Choose a class and "create assignment" from the dropdown menu and click "Go" (5). Last, name and describe the assignment and click "Assign" (6) to distribute it to your students!
(1) Profile page - Projects folder (click the three dots to open up the project dropdown menu)
(2) Projects folder - Create assignment
(3) Create assignment dialog window (you might have to scroll down to unveil the Google Classroom icon)
(4) Google Classroom icon
(5) Google Classroom - select a class and "Create assignment" from the dropdown menu, click "Go"
(6) Google Classroom - add name and description to the assignment and click "Assign" to distribute it to your students