You can navigate through a synth by using the on-screen navigation that you see in the upper right hand corner of a synth, or by clicking on the arrows on the screen. But there are other keyboard shortcuts you can use to get through a synth that can give you a different perspective.
The + (plus) and - (minus) keys will zoom in or out around the center of the window.The ← and → keys will move you left or right to a neighboring photo, while u or j will move you up or down.
You can use the spacebar to go to the next photo in the tour, or Shift-spacebar to go to the previous photo. It can also be pretty revealing to go through the photos in alphabetical order by filename--which is usually the order in which the photos were shot. Use the period (.) to go to the next photo in alphabetical order, and the comma (,) to go to the previous one.
Small z will go to the last image you were on, much like using the back button in a Web browser, while capital Z is like using the forward button.
Want to see a synth the way the computer sees it? Hold down the control key to hide the photos and see the point cloud. If you drag a halo (that circle in the center of the screen) while holding down the control key, you'll be able to spin all around a point cloud (note: you may not see the halo on every synth). The P key lets you toggle among three modes: point cloud, images, or both. Check out the point cloud on this flower or on National Geographic's synth of the Sphinx. It works better when you zoom out a bit. Try it.
The tilde (~) lets you toggle between the 2-D and 3-D views of a synth. When you're in the 2-D view, zoom in really close with the scroll wheel on your mouse (or with the + key, right?). And f lets you toggle into full-screen mode.
If you forget, the full list of keyboard shortcuts is at the end of our Photosynth photography guide.