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Go to your course and turn editing on.  Add an "Assignment" activity. Fill out the following sections.

General: 

Give the assignment a name and fill in information about the activity in the description.  

Assignment settings: set

Set up the due date and optional opening date cut-off dates.  If you enable the cut-off date, students will not be able to submit their work after that time.  There are lots of other options here.  You can click on the question marks next to the choices to get more information on what each control does.

Submission settings: 

Select what type of assignment you want.  The main choice is whether you want students to enter online text in a box in Moodle or upload a file or files (or both). 

Feedback Settings: 

Enable feedback comments or files here.  An instructor can send a feedback message to a student or upload a response to the student.  For example, it is possible to download a student's MS Word document, turn on track changes, enter feedback right into the file, then upload the marked-up file as feedback to the student.

Grade:

If using the online gradebook, can set up grade information here. If you are not using the Moodle gradebook, but will be providing feedback, select something other than "No grade" so that the grading and feedback screen appears.  

Common Module Settings and  

Usually no changes required 

Restrict Access: usually

Usually no changes required 

Student Submissions

Students will see the assignment link from the front page of Moodle.  They will be able to click on the assignment and enter their text or upload their files.  Moodle will give the student information about the due date and the current status of their submission (not yet submitted, submitted, graded, etc).

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