Create your assignment document. You'll want to make a copy for each group that you intend to have. To help organize, add "group 1", "group 2" and so on to the end of the file name. Create the assignment as you usually would. Give it a title, add instructions, and attach your document for your first group. Then, click where it says all students.
You'll see a dropdown box with the name of each student in the class. Un-click the box next to "all students".
Check only the name of the students in a particular group. Make sure that instead of "make a copy for every student," you'll want to choose "students can edit". This way, all students in the group will be working on the same doc, and each student will be able to click "turn in" when the group is finished.
Here's the rub to using this method: You'll need to repeat this process for each group you want to send a document to, each time attaching the document you created for that group. You cannot assign the same original to every group, otherwise all groups will be editing the same document!
As always, feel free to reply with any questions!