Eliminate cover sheets. Items like Post-Its for faxes work just as well and don't use an extra sheet of paper. Don't print a confirmation sheet. If your fax machine does this by default, the manual should say how to disable that feature. Fax to and from your computer.
Many computers are capable of sending and receiving high-resolution faxes, and it requires no paper.
Use recycled paper and recycled toner in your fax machine. Turn the fax machine off at night if your office doesn't receive faxes after hours. On many fax machines it is also possible to set a timer. Turning the fax machine off at night conserves energy. Look for energy efficient models when you buy your next fax machine.