You don't need any extra software.
The best way to do this would just be to email yourself the PDF. The iPhone can open the PDF in the email, and display it.
You can also use apps like GoodReader to open it as well, so that you can somewhat store it on the phone. If you have that app (or some others) installed on your phone, you can hold down on the PDF icon in the email to save it and open it in one of those apps. If you have one of these apps installed too, you can drag the PDF to the app in iTunes when syncing your phone (although, this is much more complicated than it needs to be).
iBooks also lets you save and read PDF's. You do the same as above, either hold down on the PDF icon, or when its open, click the share (looks like an arrow coming out of a box) button to open in another app. (Its the icon in the bottom left of this picture)
As for where you note that you don't see the iPhone drive, iOS doesn't do this like Windows and Android phones do. You may be able to enable the iPhone as a drive, but it can't access that data, without possibly jailbreaking or the like.