As a first step in dealing with your child's sucking habits, ignore them, because most often they will stop on their own. Here are some other tips to get a child to stop sucking their thumb or using a pacifier.

No matter what method you try, be sure to explain it to your child. If it makes your child afraid or tense, stop it at once.
The good news is that most children stop their sucking habits before they get very far in school. This is because of peer pressure. While your child might still use sucking as a way of going to sleep or calming down when upset, this is usually done in private and is not harmful. Putting too much pressure on your child to stop may cause more harm than good. Be assured your child will eventually stop the habit on her own.

Praise and reward your child when she does not suck her thumb or use the pacifier. Star charts, daily rewards, and gentle reminders, especially during the day, are also very helpful.
If your child uses sucking to relieve boredom, keep her hands busy or distract her with things she finds fun.
If you see changes in the roof of your child's mouth (palate) or in the way the teeth are lining up, talk with your pediatrician or pediatric dentist. There are devices that can be put in the mouth that make it uncomfortable to suck on a finger or thumb.