To send a fax, you simply open your Google Docs document, then click the “Fax This” bookmarklet (which you can add to any browser). Type or paste in the fax number and presto: the document gets delivered. In my tests, it took just a few minutes for outbound faxes to arrive.
Now, if you’re talking about actual paper documents (as opposed to electronic ones), you can scan them into your PC, then deliver them via e-mail or use an outbound fax service like Fax.com or MyFax. For about $10 per month, you can send and receive an unlimited number of faxes, using your computer as the “fax machine.”
If you don’t yet own a scanner, I recommend investing a multifunction printer (one that can copy, print, and scan) that has an auto document feeder (ADF). You should have no trouble finding one for under $100.
With that piece of hardware and one of the aforementioned services, you’ll be able to send (and receive) faxes to your heart’s content. There may be an extra step or two along the way (i.e. the process of scanning and then sending), but you definitely won’t need a landline.