Even children who do cooperate in brushing their teeth usually do it quickly and only for the good taste of the toothpaste. To teach them to brush properly, you can purchase disclosing tablets or drops at a pharmacy. When the tablets are chewed, or the drops are swished around the mouth, they will highlight any organic material, i.e. germs, and will very dramatically show the child where the "dirt" on his teeth is. Let the child have the tablet or drops after he has brushed his teeth; then, using a light and a hand mirror, help him examine all of his teeth's surfaces. The spots that are white have been properly brushed. The spots that are red have not. Have the child brush again and try to eliminate all the red spots. Do this daily at first and then weekly just to check.
If this procedure along with explanations that excess plaque can cause gum infections and tooth decay, still do not motivate your child, try investing in an electric or battery-operated toothbrush. These not only do much of the work of tooth-brushing but are also fun for kids.
You should be aware that until the age of six, most children do not have the coordination needed to brush their teeth properly. While they should be taught and encouraged to do so, a parent needs to go over the teeth to make sure they are clean.