Begin with a visit to your Dentist.  Dental professional will teach your child the proper way to brush, using "kid-friendly" words.

Let your child select their own toothbrush and toothpaste.   Many colorful child-sized toothbrushes are available on the market, as well as toothpastes in flavors that appeal to kids.  However, make sure that the toothbrush has soft or very soft, rounded bristles so they do not damage your child's gums or tooth enamel.

Be sure your child uses only a very small amount of toothpaste on their brush.  Kids tend to swallow toothpaste, and it is important that the child does not receive an overdose of fluoride.  If your child does not like toothpaste, you can always depend on that changing.  In the meantime, you do not want your child's dental hygiene sessions to turn into a battle.

If your home has more than one bathroom, keep a toothbrush and toothpaste for the child in each one to facilitate making brushing more convenient.

Brush your pet's teeth, and let your child help - or at least watch.  Not only does this reinforce the idea that clean teeth are important, it is also good for your pet.
 

Praise your child's brushing efforts and the results they are producing.  Try saying "Your teeth are so sparkly!" or "Your breath smells so good!".  They will be delighted that you noticed, and the positive effects of brushing will be reinforced.

Try sharing some books about dental hygiene with your child.  Some good ones are Dragon Teeth and Parrot Beaks - Even Creatures Brush Their Teeth, by Almute Grohmann, and Just Going to the Dentist, by Mercer Mayer.

You and your child can make up silly toothbrushing songs set to familiar melodies like "The ABC Song," "Mary Had a Little Lamb," or "Row, Row, Row your Boat."
 

And finally, because children learn by example, be sure your child sees you brushing and flossing your own teeth every single day. It's good for them, and good for you!