Many of us would have been better off financially in life if we had started learning about it as children. Unfortunately, the most education that many of us got was a brief section here or there as part of some class. There really should be more to it than that.
The people who are most responsible for the education of the children are the children's parents or guardians. Sure, these folks may not have the best education for this stuff themselves, but they must still try to make sure that the kids learn enough at the right time.
One of the easiest ways is to include the children when paying bills. How many times have you sat around the table figuring out how much you have to pay for basic utilities, rent, food, and so forth? Do you sit the kids down with you? Maybe you should.
Once the children are old enough to communicate verbally and can understand cause and effect, you can start showing them the finances. You can make a small stack of something to represent your income, and then move the items from that stack to another representing each bill as you pay it. Before too long, your income stack will have dwindled and the child may understand that money isn't an endless supply.
You must take care that this doesn't become depressing to the child. All gloom won't help anything. Instead, focus on how a thrifty lifestyle can lead to choices for better purchases later. Just as important, this formal little exercise in accounting may lead you to do better with your own budgeting.
Outside of including your child in the bill paying, you should try to take advantage of kid resources available at your financial institution. Most banks have savings programs just for kids. The goal of these programs is to get the children to be good with money so they will be better customers for the banks later. Banks really do prefer customers to be good with money; it is in their best interest.
In addition to the savings programs, some banks may have educational tools to help kids learn. You can ask about them when you ask for educational tools for yourself.
In general, money earned has more value to a child. Try to help your child earn money and understand the concept of work. This may or may not include chores around the house (some people consider chores as just contributing to the household and learning to maintain one's environment.) There's nothing wrong with gifts or allowances, provided they are reasonable and do not become an expectation in life. A kid is better off with a reasonable job.
It is also important for the child to understand why you have to go to work and how that relates to how you are able to provide food, clothing, shelter, and toys. There should never be a concept of something for nothing. The child must also understand his or her responsibility to the child's descendents and how productivity ties into that.
As much as you can, help your children learn about finance as much as they can while they are young. When they turn eighteen, it is too late; they should already be prepared. Who knows, if you do a good job your children may be able to take care of you in your old age.