The most practical way to do this is via an e-mail faxing service/server. In essence, you e-mail what you want to fax, with the phone number as the subject. The server receives the message and faxes the attachments for you.
There are services like RapidFax and FaxAway which are both pay services.
Here is a pretty good guide Internet Faxing Guide as well. It looks like it might even have a couple of free options.
I remember looking into this a few years ago with different results. I had found a voicemail/fax program that could be loaded onto a computer and would fax documents that were e-mailed to its special account. The software wasn't too expensive, but I had a b!tc4 of a problem betting it to work reliably. The nice thing about it was that it could also be my fax machine and voicemail system. You could actually set up voicemali boxes for each person and it would e-mail you the voicemail messages and faxes. I don't remember the name of the software - it was too big a hassle to keep it up and running reliably.
I'm sure there are other fax programs that may do this as well.
