I actually called my father, a dentist, about this question. Make sure to get the softest toothbrush possible as buying harder ones only injure the gums and create a place for plaque to attack the teeth (this is the same for adults as well, only use the harder toothbrushes for cleaning your house). Use baby toothpaste because they can swallow it. Brush in circles, make sure to get behind the teeth as well as the front and do this twice daily. And actually fluoride is extremely important for your child to get. Check to see if the water company where you live puts it in your water, if they do, then you don't have to worry. Otherwise call your dentist and ask what can be done to get your baby exposed to it. My father warned that he has taken many a toddler into surgery because he/ she has had so many cavities that he had to put them to sleep. At around 3 your child should have his/ her first checkup and cleaning.... hope that helped.
Also you can use a dot of toddler toothpaste if you want him to get some flavor, it doesn't have fluoride and is safe to swallow. My son liked it and it made brushing time more enjoyable for him. Basically there's no way to ensure they don't swallow it at this age so you shouldn't use toothpaste with fluoride.
I have known Moms who clean them with a soft baby brush at this age , no paste just warm water ,its a good habit to get them doing you do it and let the baby hold the brush and try , so you are making a happy game with it,he or she will laugh and enjoy doing it .