Positive reinforcement is something that parents use all the time with children. This can be something as simple as praising your child when he or she acts in the way you want. So, if you want your child to stop sucking her thumb, when you see her not sucking her thumb (in a situation where she often does suck), you can praise her. This is something she will value and it will positively reinforce her behavior (of not sucking her thumb).
Negative reinforcement is less common since it involves removal of some unpleasant stimulus when your child does what you want. The most common example of this would be removing some behavior of your own that the child does not like. In other words, if your child hates being constantly reminded to clean up her room, the removal of the nagging when she actually does clean her room would be an example of negative reinforcement.