Parents often name themselves as custodians. You can also buy a few shares of a company your kids know and like. If your spending limit is higher, buy two shares, or five or 10. That involves buying stock directly from the company. But shop carefully.
Some companies require high minimum investments or impose stiff fees.
For kids, you can pick one of several funds designed for young beginners. For any age, you can pick any of numerous funds with a good track record, low expenses and a low minimum initial investment. Most provide educational materials for young investors. These are the old reliable money gifts from grandparents, uncles and aunts. They are among the safest investments around, and there is no charge for buying them.