Short answer: Unfortunately, you cannot easily fax directly from your iPhone without using a third party service such as eFax, myFax or the many clones like them out there.
The long answer:
What you would need to make faxing directly from the phone work is called Circuit Switched Data (CSD) . The hardware inside the various iPhone models technically supports it, and technically, so do most parts of the legacy Cingular/AT&T wireless networks.
But, you've got two obstacles to overcome before you can make it happen. First, you need to get AT&T to provision CSD ono your account. that's going to be ahrd to do since they've been trying to get rid of CSD altogether for a long time now.
Second, you would need software that would make the iPhone accept AT Faxmodem commands from a USB link to your computer, or issue those commands internally if you're picking your documents from within the iPhone. That same app would need to be able to connect with the internal modem when you're receiving faxes, and convert the data into a PDF or some other type of document. Considering what's involved, I have a feeling Apple probably wouldn't approve such an app, leaving you to have to make it a Cydia app or something like that.
Considering I haven't really seen any such apps for the iPhone, it's probably either pretty hard to do, or isn't something that enough people are even interested in anymore. it's probably a little of both.
Given all that you'd have to do to make it work, you'd be better off googleing the many fax-to-email companies out there and singing up with one of them.