Faxes are the technology that won't die. Having become popular in the 1970s, they persist in modern business, despite being redundant and needlessly complicated. Increasingly, fax capacity has been transferred online, often via office suites. In keeping with this norm, OpenOffice.org offers everything you need to fax from within it, but you do need to do some configuration both inside and outside OpenOffice.org before you can use the office suite for faxing.
You can use a stand-alone fax machine with GNU/Linux, but you quickly run into the problem that it probably connects through the modem -- and the vast majority of built-in modems these days tend to be Winmodems, so-called because they required a running copy of Windows to use. You can learn how to test your modem from Linmodems.org, and, in some cases, how to get it to work despite its design. Another alternative is to scrounge a ten year old external modem from a second hand store, which has a good chance of not being a Winmodem.