For children aged 3–10, the right amount depends on the child's age. A common general guideline is a pea-sized amount for children in this age range. The product itself advises using the appropriate amount for the child's age group, so if your child is closer to 3, start with a smaller amount and adjust as needed. There is no need to cover the whole brush head; a small amount is enough.
Brushing should be supervised according to the child's age. Younger children may need help to make sure they spit out the toothpaste rather than swallowing it; they often lack the coordination to spit reliably on their own. Older children can brush on their own but may still need a reminder to rinse and spit. Encourage the child not to swallow toothpaste and to rinse well after brushing.
If you are unsure how much to use for your specific child, a dentist can give individual guidance.