The modern approach to children's dentistry is prevention orientated
Take your child to the dentist regularly and take them with you when you visit. Do this right from the start. Don't wait until they are 3 years old or more. If you waited until this age to take them to the supermarket they would be scared about going there rather than visiting the dentist.
Start as soon as they get teeth - they may not like it !
But they soon get the hang of it !
It is much easier to brush children's teeth while they are standing up with the adult standing behind. The lips and cheeks can be moved aside to aid cleaning with the hand that is not holding the brush.
Before deciding on whether to give your child fluoride supplements you will need to check the level of fluoride in your water supply.
The more fluoride your child gets while the teeth are forming the more resistant they will be to decay later. There is a downside though - Increasing the fluoride increases both the likelihood and the severity of dental flourosis.
There is also a downside with respect to "occult caries" - decay within a tooth that looks perfectly OK from the outside. This happens because the extra fluoride makes the outer layer of enamel very strong. It also strengthens the inner part of the tooth, the dentine, but to a much lesser extent. This makes it unlikely that the tooth will decay, but if decay does start and gets to the inner dentine, the decay will spread inside the tooth and the extra strong enamel shell will remain unaffected. Huge holes can result if regular radiographs are not taken.
You should discuss these things with your dentist but in the end it is your decision.