They will learn the importance of saving towards future goals and gain the self discipline and skills that so many people lack in today's society. Start an allowance when a child starts elementary school. School signals the beginning of important responsibilities for children. Being late implies it's OK to be irresponsible. Distribute allowance at the beginning or middle of the week.
Most kids spend most of their money on the weekends.
Giving early in the week forces them to think about how they'll spend it later. Make the allowance large enough so that some of it can be saved. It will also give the child an opportunity to develop a need to save. As children get older, increase their allowance and what it should cover. This gives them more experience managing larger sums of money to make choices about how to spend it.