Students can submit assignments by visiting the assignment activity in Moodle.
They will see a submission button (if submissions are open).
Depending on what has been set up by the teacher, a student may be asked to upload a file:
And/or write some text directly into Moodle:
When they are done they click "Save changes".
They are then given an overview of their assignment, which they may or may not be able to edit depending on the assignment settings:
Once the teacher has graded the assignment, this view may change to something like this:
And feedback appears underneath:
» Guide to Moodle