Although I am explaining the system we use for Dropbox, any Cloud service or network server* will work the same.
We save almost no paper, even work-in-progress may have to be referenced from the cloud.
The first level of folders in our system are the main aspects of a design firm:
Before focusing on Projects, let me say that the Standards folder holds all of our Reference files, like codes, our Templates for everything from letterhead to change orders, and Procedures files that explain how to do stuff.
The Projects folder is the most complicated. The graphic shows the arrangement that every project starts with so that there is some uniformity. The folders at the next lower level tend to adopt the character of the project. So, for instance, there may be a separate folder for zoning and additional folders for phased permit applications.
Of course the actual names are not crucial, just the fact that there is a system and that you can depend on files 'being where they should be'. The names you see here are pretty self-explanatory with the exception of 'backstage', which is our designation for all the stuff that is somewhat private. Backstage is where we keep a copy of the contract, proposal letters, consultants proposals, invoices and accounting reports, fee calculations, etc.
The 'zarchive' folder, so named so it appears last, is where files are moved as they become obsolete. This is not always used, but it gives us a place to put things on-the-fly that have gotten in the way.
Somewhere between 10 and 20 items in a folder, confusion sets in and we reorganize into a new group of subfolders. The one exception are the dwg files, which remain easy to find regardless of number because our file naming convention for them is ABCD0A201. 'ABCD' is the project ID that is used for everything. '0' is a version ID in case one is needed. 'A201' is the sheet designation. If you are using Revit or ArchiCad or VectorWorks, this is taken care of within the project database.
The beauty of developing and using a system like this is that even years later, you know exactly where to look for a file.
* I think network servers are a millstone around your neck. You buy a server-grade computer, a battery backup, server software, client licenses, a tape or cloud backup system. You pay to have a firewall and a VPN set up. If you did it right, you can access all your files over the internet. If you didn't, oh well.
We would spend at least $500 per year having this setup "worked on". For just about the same cost per year, we pay for monthly subscriptions to Dropbox, who in turn buys the servers, battery backups, etc and we get access to all our files wherever there is internet service or 3G/LTE service for our phones/tablets (like on the job site). I will admit that I am oversimplifying, but not much, and not about the costs and aggravation.