iPhone save PDF file and view it

You need to use iTunes to transfer it to the app on your iPhone that will take ownership of it. The simplest solution is to use iBooks, which you can find in the App Store on your iPhone if you haven't downloaded it already:

1. Drag the PDF into iTunes
2. Select your device on in the left hand pane, then select "Books" on the top.
3. Make sure "Sync Books" is checked, and if you're syncing selected books, check the check box by the PDF you just added.
4. Hit Apply

The PDF should now be in iBooks on your iPhone.

If you use Dropbox, you could save the PDF file from your Mac, and (after Dropbox syncs) read that PDF file from the Dropbox app on your iPhone.

Provided you have internet connection, the pros:

1. you only need one copy of the file (at Dropbox) without creating duplicates and using up memory.
2. you can replace a PDF with an updated PDF and let Dropbox takes care of sync'ing it to your other devices.
3. Dropbox is free
4. iTunes not needed (and if you set iTunes to backup the device on your Mac's hard disk, then the PDF file(s) will use up hard disk space).

The cons are:

1. Dropbox does have a limit to how much storage it allows for free
2. you need internet connection and will incur telco's data charges unless you use WiFi.

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.