Firstly, if the gallery refuses to load the first time you try that section of the iPhone app, try switching your phone off briefly. This appears to be a caching issue, but if that doesn't work, try uninstalling the app and downloading it again from iTunes. Note that an internet connection is always needed when viewing the gallery.

Once you successfully get the gallery to load, you'll be met with a splash screen that looks similar to this....

In the image above, where you see the text "All albums", there is a small button. Tap on this and an album will load. Next, tap anywhere on the screen. In the image below, you can see an album has started playing and the screen has been tapped once. If you click on the icons next to where you see a "1", the albums available to you will load. If you tap the icons near the "2", the images for this album will load and you can scroll through them to jump quickly to another image...

Below, you can see that the Album icon has been tapped and now there are albums listed at the top of the screen (in this image, "Covent Garden 2010" and "Regent Street London"). You can scroll through these with you finger (by swiping left or right) and then tap one to open that album...

And that's all there is to it. The images load and you can also swipe through these to view each image, or tap once on the screen to bring up the 'next' and 'previous' buttons.