If your printer does not have Air Print capability, you can still send a Fax from your Macintosh OSX using an external Fax Modem.
In this case you will need the US Robotics USB Fax Modem, model USR5637. Go to the USRobotics website, click buy and you'll have your choice of several vendors. I chose Dell. It was delivered reasonably fast, and as advertised.
The setup is a little tricky, but not insurmountable. USRobotics doesn't offer much help with anything beyond the basic installation: i.e., plug modem into usb port and phone jack, and install the Mac software from the CD that comes with the modem. This is just the beginning, however. Next you must configure the OSX software to recognize and configure the modem. That's what USRobotics doesn't tell you how to do.
There are two main steps.
- Make your Mac aware that it has a Fax Modem attached. You do this in the Network control panel, accessed from System Preferences.
- Configure your Fax Modem in the Printers and Scanners control panel.
Pictorially, here's what the steps look like:
After installing the USRobotics software from the CD, go to the Network control panel. You should see an entry for a Fax Modem in the left pane:

Type in a name for the Configuration, or leave it at Default. Then type in YOUR phone number - the phone line to which the fax modem is connected. I left Account Name and Password blank. Then you MUST click on Advanced button. This takes you to a drop-down or tabbed dialog that looks like this:

This step is important. From the Vendor drop down select USRobotics. From the Model select USR5637. Select Enable Compression and Error Correction check box. Check Tone (assuming you have Touch Tone service) and Sound On (although the Mac doesn't let you hear any sound; ask Apple why not.) Click OK. Return to the previous Network Control panel (previous screen, above). Click Apply. Then close the Network control panel.
Next, you must add the Fax Modem to your list of Printers, Scanners, and (now) Faxes. Open System Preferences, select Printers and Scanners and in the bottom of the left pane, click the "+" symbol and Add your new Fax Modem, which is called "USB Modem" (because your new modem actually can do more than just fax. But that's another topic):

In this dialogue, check the box "Show Fax Status in menu bar."
To actually send a fax, open either a PDF document or a Word Document. In the lower left corner, from the Print options, select "Fax PDF...". Here's an example of what you might see:

From here you will be taken to another print dialog where you will be asked for the Phone Number of the destination (the "To:" field).
HP offers a FaxBack Fax Test System. Prepare a one page test document and send it to them at 1-888-473-2963. If the fax was sent correctly you'll get a phone call back in five or six minutes with a fax acknowledgement.. So be sure you have configured Received Faxes in the Receive Options dialog tab, shown in the screen previous. (You'll find your received fax in /Users/Shared/Faxes which is the default location that you can change.. Curiously, I had to empty the received folder before I could get another HP FaxBack reply. I don't know if that would be necessary with other received faxes.)
I hope this helps you and others who are puzzled on how to send and receive Fax documents from your OSX device. Faxes are still useful. My medical provider only accepts documents by US Postal Service mail or by Fax, not by email. So the day of Faxing is not yet over.