As teacher you can add the function Assignments to the Content menu. This function allows you to create a webpage to describe the assignment, give instructions and deadlines and allows students to turn in the assignment as an uploadable file or as text written in a comment window.
The Progress tool can be used to check, grade and give feedback on an assignment. You can also choose whether the assignment is part of one of the goals stated in Progress and course objectives.
Urkund, for plagiarism control, can be also be used for assignments.
When you create an assignment you should first choose whether grading will occur anonymously or not. You can even select whether the assignment is to be done individually or in a group. It is not possible to change these settings after the assignment has been saved.
If the students are working on a group assignment it is only necessary for one of the students to upload the file for it to be counted for all of the group members. Even the marks or grades will be noted for all of the individuals in the group. Note that anonymous grading cannot be used for group assignments.