A completely paperless office isn't really possible (you need to keep hard copies of receipts, tax materials, signed documents and the like); but you'll be doing your pocket and the environment a good turn if you can use less paper: Cut down on the number of pages you use instead of cutting down more trees for paper.
There are a number of solutions for minimizing paper use. Some have to do with the way you think and act --like throwing the paper that you don't actually need into the recycle bin and only printing when absolutely necessary -- and many have to do with technology.
Many companies now let you receive and pay bills online, with no need for paper copies (or for standing in line at the bank). Your office can also send bills via email and use accounting software to track finances. To save paper, scan pages of non-electronic materials. You can save some information as PDFs, and there is software available that can convert scanned documents into text. Use an electronic faxing service so you can both send and receive faxes via your computer without the need for hard copies.
You will need a user-friendly system for document filing. This needn't be any harder for electronic documents than it is for paper ones. There are systems that you can buy; some are intended for large companies, and some are more appropriate for home offices and private use. Or simply be sensible about creating document and file names for easy retrieval. You should also consider information security, and be sure to have updated anti-virus and firewall protection. Be sure to back up your system regularly, whether onto CD, USB flash drive or another removable source.
A (nearly) paper-free office isn't something that's easy to set up from one day to the next, but in the long run, it's worth it. Just the saving on printer ink can be quite significant. Additionally you use a lot less space and make a lot less mess when you don't have those piles of paper to deal with.