Storing Files in Canvas: Is "Files" available to your students on their menus (on the left side of the page in Canvas?) If not, you can go into your Canvas course (as the teacher,) click on "Settings" and then on "Navigation." Drag "Files" above the line that says, "Drag items here to hide them from students," so your students can see them.
From my student account, I can click on "Files" and then at the bottom of the screen I can click on "All My Files." From there I can upload files.
The correct solution is to have all your students save their documents to Microsoft OneDrive or Google Drive until they are ready to turn them in. There will be many fewer steps, and this is how the technology is supposed to work. It is also how 90% of the world does things.
I don't know if your school uses One Drive or Google Drive more, but asking them to use the one they are more familiar with and that their student email is linked to will yield much better results.
It is possible to turn documents into Canvas directly from OneDrive or Google Drive.
Integrating OneDrive or Google Drive in Canvas: Go into your Canvas course (as the teacher.) Click on "Settings" and then on "Navigation." Do you see "One Drive," "Office 365," or "Google Drive?" If so, please drag them above the line that says, "Drag items here to hide them from students," so your students can see them.
Then, ask your students to give it a try. They will need to authorize Canvas to access their OneDrive or Google Drive, and it looks a bit scary. After they authorize it and play with it for a few minutes. They will figure it out.
It might be easier to have your students download the document from OneDrive or Google Drive and turn it into Canvas from there.