Sometimes it's just not possible. Your instructors may be less inclined to use the internet and electronic resources and instead give you notes or assignments on paper that you'll need to keep. Also, tests and assignments that you'll receive back will be paper. So make sure you have at least a couple of folders on hand for organizing these.
What I did to avoid as much paper as possible was this: I created a separate folder for each semester on mu computer. Within that folder, I created a folder for each class. Most of our instructors uploaded documents like the syllabus, notes and assignments to our schools' email center. I just downloaded the forms from the website and saved them in each folder. When I was working on assignments, I saved them in the folders.
If you wanted to go one step further than I did, you could get a scanner. When you get papers from your instructors, scan them to your computer and save them in the right folder. Then you'll have them for reference without needing to carry around the physical papers.