When one say they buy stocks for their child/children, how do they actually do it when the account can only be set up for 18yo & above?

Parents can open custodial accounts for their child and then following which they can purchase shares on their child's behalf

Theres something called a custodial account which segregates the investments from the adult. The parents can contribute money to the account but the investments is owned by the child, although that money can't be touched until the child comes to age (18).

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Im 13 and I personally use a youth account. My parents can supervise my investments but I have full access to my account. Depending on your perspective, both accounts are rewarding although a youth account is more interactive.