I use Dropbox for assignment submission and return. You do not need to install Dropbox on your computer, though you may. This sounds like I'm a shill for the company — I assure you, I have no connection other than being a happy user (my stepson did apply for a job there but did not get hired :().
Dropbox is a cloud-based (meaning the storage is "out there" somewhere and you connect to it via the internet. The service allows you to designate a folder on one computer that will be automatically "sync'ed" with the folder on another. The main use is so you can have the same data on multiple machines (e.g., your laptop, your desktop, and your phone). Another use is for people who want to collaborate to share a folder. That's how we'll use it. I'll invite each of you to share a folder; there will be a folder on your machine and a folder on my machine. If you put a document in the one at your end, I see it at my end. You submit an assignment; I see it; I comment on it; You see my comments. No delays, no paper, no hassle.
An added advantage if you actually install Dropbox is that files never go away. You can always recover a file even if it's been deleted.
Here's a short tour of how it works.
You can get dropbox by going to the website and downloading. Alternatively, someone who has dropbox can invite you (and then when you get Dropbox they'll get a bonus).