A child of between the ages of 3 years old to 6 years old only needs a pea sized amount of toothpaste to brush their teeth.
Also a child of 3 to 6 years old needs a child sized toothbrush and should be supervised while brushing their teeth to ensure they do not use too much toothpaste and also to make sure the child does not swallow the toothpaste either.
Once the child gets above 6 years old then they can use a bit more toothpaste and use a bigger toothbrush and then at 7 years old and above you do not really have to supervise them while they brush their teeth unless you want to ensure they are actually brushing their teeth and doing a good job.
You can also and should also brush a babies teeth with just a tiny smear of toothpaste to keep the babies teeth clean.
After the child gets above 10 years old then they can brush their teeth with as much toothpaste as they need but all they really need is to cover the toothbrush with toothpaste which is enough.