Using the directional scanner is one of the most important skills in the game, if not the most important. If you want to be a solo pvper or even a fleet tackler you must get good at using the directional scanner.
The directional scanner is both a offensive and defensive skill. It's all about knowing what is around you and having "situational awareness."
The more you know about your battlespace the better you will do, period!
In the following video I cover all the basics of using your directional scanner as well as some more advanced tips and tricks.
The most basic things you need to understand are than it works on range and direction. Your maximum range is about 14au and you can alter the angle and direction of your scanner to find the range and direction of the target.
The absolute best way to learn is to go to high security space and start scanning miners in belts. Do this over and over until you can find them very quickly. Then move on to finding people in anomalies using the tips in the video. Also, make sure you get your overview settings setup in a way that helps you to scan faster.
Watch in full screen in 720p for best quality.