Hit "s" when the camera is selected to key its position/scale/rotation etc. This will automatically key each of them. If you want to only key Rotate X, for example, click Rotate X on the right of the screen so it's highlighted blue, then right-click it and select "key selected". Either way you'll see a red line appear on the timeline, signifying a keyed position.
On the lower right of the screen, there's a key - if you click that on (so it's red), and go to a different point on the timeline and move the camera, it will automatically key the new position. If it's off you'll need to hit "s" again to key it. Scrub along the timeline between the keyed points to see the camera move.
If you want to control the transition between points, like have it start slow and speed up, etc, open the graph editor under Window/Animation Editors. With the camera selected, you'll see a graph of all of its keyed points. Play around with the icons on the top of the window to see how each will affect keyed points.
Also when you select your camera, in the toolbar on the left the manipulator tool will show up. If you drag its center of interest and then move the camera, it will always stay focused on the center of interest. Good for spinning camera moves etc.
Finally if you create a curve (create/cv curve tool), you can draw a curve the camera can follow. Once drawn, select the camera, shift-select the curve, then in your animation toolset go to animate/motion path/attach to motion path. You might need to play around with the xyz settings to make sure it's ponting the right way. But then you can have flying camera moves.