Here is a pretty useful article on the correct way to use poles.
There are several aims in using a pole. In my opinion, the primary one is to reduce strain on the knees and ankles. Additionally they provide extra stability on rough ground and can make going uphill easier. The disadvantage is they result in extra weight and may increase total energy consumption, although hiking may still seem easier as the extra energy is coming mainly from your arms.
When holding your pole you should aim to have your arm horizontal with a 90 degree bend at the elbow. This allows you to generate maximum force in the pole. If you have an adjustable pole adjust it so that it is the correct length, otherwise just adjust your grip position.
When hiking you want to plant the pole so that you can load it with force to either propel you or lessen the impact downhill. For flat/uphill walking this means placing the pole angled slightly forward with the bit on the ground pointing towards your body. This makes it easier to push forward on the pole. Going downhill, do the opposite. Point the pole away from your body, then push on the pole, lessening the impact on your knees as your foot lands.