For younger children, the most useful starting concept is simply that money is finite and comes from work — a basic allowance tied to small chores, with the freedom to spend or save it themselves, teaches the trade-off between spending now and saving for something bigger, in a low-stakes way.
For pre-teens, introducing the idea of a savings goal — saving toward something they actually want, tracked visibly, like a jar or a simple notebook — makes the abstract idea of "saving" concrete and rewarding rather than just a rule imposed on them.
For teenagers, opening a basic bank account in their name, and involving them in real conversations about family budgeting decisions at an appropriate level of detail, helps translate childhood habits into the practical skills — reading a bank statement, understanding a simple budget — they'll need once they're managing money entirely on their own.