Thumb sucking is one of the worst habits that parents have to peel their children away from after nail biting, temper tantrums and the cooties. If this is not stopped at the early stages, it might prolong to their childhood which can be embarrassing both to the child and you.
One way to do this is to give them something else to chew on. The best fix is a pacifier or maybe one of their toys as long as it does not have sharp edges. Babies begin to suck thumb since they have their new teeth coming and that makes them feel strange and want to chew or suck on something. This grows as a habit in children that they just can't give up on.
Rewarding your child with something they like usually works. Fix a goal everyday which when your child reaches, they will be rewarded with something they don't always get. Another way to fix to is to make their thumb taste bitter. You can rub their thumb with a bitter oil, like eucalyptus oil that tastes extremely bitter in high concentration.
Just dab their thumb with a cotton swab or a cloth dipped in a bitter tasting oil. This will remind them to keep their thumb away from their mouth. If you think they would simply wash their hands to get rid of it, you can paint their nails with something bitter and something that can be removed when you want to.
Keep their hands busy so they will be distracted with sucking the thumb for a while. This has less chances of working but it still prolongs time time when your child is not sucking the thumb.
Try letting your child play with other kids who don't suck thumb. When he finds himself surrounded by people who don't do it and realizes that he's the only one with the habit, he'll begin to put effort into letting go of that habit and maybe even ask you for help.
Remember not to yell, compel too much or punish your child for it. You should know that they don't realize it's not a good habit and if they do, they are so habituated to it that they can't stop even if they want to. And this is where you step in and take initiative to break the habit.