First of all, teach children that our blessings come from God. Money is a gift that we are given to use wisely. Jesus taught some parables concerning money and these are wonderful Biblical examples of how to handle money. (For examples: Matthew 18; 25 and Luke 15 among others.)
Because money is from God, we should first give back to Him (1 Corinthians 16:2). Many people give to God out of what they receive and forget that God should come first before the government gets their taxes. We should teach our children that God should come first before everything else (Mark 12:30).
In our household, the children are given about 5 jobs that they must complete daily (or most every day) in addition to their regular chores. They must complete these jobs to earn the money. Then, they have a few jobs they could choose to do for extra money. I look at it this way: in life, when they have a job, they have certain jobs they have to do, but there are always extra jobs (overtime opportunities for example) that they could choose to do for extra money. According to Dave Ramsey, you choose a few jobs (less for younger children) and you assign a monetary value to it. Say, if they fold the towels they get $.25. Each time this job is done, mark them down on the chart. They are paid on Sunday evening (sometimes Monday at our house because Daddy has to go to the bank and cash his check before kids are paid) and they set aside their money for God for the following Sunday. This teaches them restraint. That money is in their 'church' bank and is not theirs, but belongs to God.
"But godliness with contentment is great gain. For we brought nothing into this world, and it is certain we can carry nothing out. And having food and raiment let us be therewith content. But they that will be rich fall into temptation and a snare, and into many foolish and hurtful lusts, which drown men in destruction and perdition. For the love of money is the root of all evil: which while some coveted after, they have erred from the faith, and pierced themselves through with many sorrows. But thou, O man of God, flee these things; and follow after righteousness, godliness, faith, love, patience, meekness."
(1 Timothy 6:6-11)