A question, you most-likely won't ask until you are a parent is, "is children's toothpaste different than adult toothpaste?" The answer is yes! The most obvious difference is in the flavors (bubblegum / watermelon for example), but the branding (for kids) is also evident. Cartoon characters make the product more enticing to children, and that encourages them to brush more often and for longer periods. The dispensers also tend to be easier to dispense for small hands, and often stand up to make bathroom sinks a bit tidier.
Fluoride has been proven to protect from future cavities, and to re-mineralize small cavities. For children age 3 and younger, use a children's fluoride toothpaste about the size of a grain of rice. Again, you can use a non-fluoride version, if they tend to eat or not swallow it. For children 3 to 6 years old, the amount should be pea sized, and they may be ready for adult toothpaste.
Dr. Frank Sierra reminds parents that, "most children don't have the motor skills to brush their teeth effectively until age 8, so should be supervised to make sure that each brushing session is getting the job done."