The first thing you've fortunately realized is that you do need the Google Plus app for your iPhone before you can even consider uploading. The regular Google Plus site reformats decently for the iPhone's small screen, but it can't see the photos actually on your phone nor can it request a photo from the camera subsystem.

Don't have it yet? Grab a copy here: Google Plus for the iPhone [iTunes link]

Launch the G+ app on your cellphone and you'll find that it has the standard five sections conveniently listed with big icons, big enough for even clumsy fat fingers to manage:

No surprise, tap on "Photos"...

The first three sections, "From your circles", "Photos of you" and "Your albums" also appear on the iPhone-formatted version of the regular Google+ site, but it's the fourth one, "From your phone" that we're interested in. Tap on it.

The photo I want to share is on the lower left, so I'll tap on it...

The result is subtle, but notice that you can easily share considerably more than just the single photo if you're enthusiastic or so inspired. A nice feature.

To proceed from this point, however, you have to tap "Share" on the top right (which I think is a bit confusing from an interface design perspective). When you do, you're prompted to enter a comment, add a location if you're so inspired, and even change which circle or circles you're going to share the image with:

I usually have my circle set to "Public" and often skip adding a location. Instead, I just tap in a quick comment, as you can see here:

It all looks good? Great! Tap on "Post" on the top right and it's up and live!

I will note here that there's a bit of confusion about how Google's implemented the camera feature in the app, because you can't get to the camera button without actually uploading a photo that's already on your phone. If you do, however, you can then take photos with the camera while within Google Plus and post it as an album. Confusing, to say the least, and something I imagine will be fixed for the next release of the app.

In any case, the key to success is to download the app, then take the photos you want to share using the Camera app before you launch Google+ on your iPhone. Then it's just a few taps away to get it all up and online for your friends and colleagues to enjoy.