A behavioral approach at the right age using a calendar, stickers, a reward, and positive encouragement is very effective for helping children learn new habits. An openbite and a large overjet may self correct when the habit is discontinued early. Crossbites will not self correct. Controlling the habit at the right age will allow the permanent teeth to come into healthier positions and prevent more difficult problems. Thumb sucking is normal until the age of 4 to 5 years.
Most children stop on their own.
I suggest that no attempt be made to stop this habit until then. At this age a behavioral approach is usually successful. Some children may find an appliance helpful. Tongue thrusting can be helped with a combination of a behavioral approach and a tongue crib appliance. The appliance is cemented in and is helpful while the incisors reposition, usually 1 or 2 years.