You can tell a directional tyre is "directional" because if you were to flip the tyres, the tyre pattern wouldn't look the same (looks like it points to the other direction).
The book usually has a nice diagram showing to cross the back tyre as they are going to the front and move the front tyres straight to the back. This way you'll get almost an even wear on all four tyres. Therefore, when the time comes, you can change all four tyres together. This is good to get the best road handling.
I usually don't recommend directional tyres for normal drivers. They cannot criss-crossed and swapped over. Directional tyres are very good for cutting through water at high speed. However, they are known to generate a lot of noise. Normal drivers tend to drive at 120km/hr max and cannot really take advantage of this kind of tyre. It is more suitable for racers and pros. I prefer to choose a tyre that is quiet (ie good non-directional pattern), long life, and absorbs lots of bumps (typically a high silica compound). I really like the feeling of driving on clouds, where noise and road imperfections are smoothed out.