Thumb sucking is natural and a normal reflex utilized by infants to soothe themselves. They generally lose interest once they develop other coping skills. Ideally, children should stop thumb sucking by the age of 4.
Pacifiers are not a substitute for thumb sucking. They, too, can affect the teeth in the same way as sucking fingers and thumbs. However, you can control and modify the pacifier easier than the thumb or finger habit.
How hard a child actually sucks on his/hers fingers or thumbs will determine whether or not dental problems will result. Some children rest their thumbs passively in their mouths, making them less likely to have problems than those who vigorously suck their thumbs.
Up until the age of 3, children are too young to actively try to get them to stop. See if they will stop on their own with positive reinforcement. Focus only on daytime thumb sucking first.
Once your child has stopped daytime sucking, then you can work on nighttime. First, your child needs to know he/she can stop at night, be positive. These suggestions only work if he/she have completely stopped daytime sucking and want to quit at night, too.