How do I share with my family and have them pay for their own purchases?

Send them down to the corner store to purchase Apple gift cards, and each should redeem the cards in their own account.

As long as they keep a sufficient balance, their purchases will be charged to their Apple ID credit, and will not hit the Organizer's credit card.

For reference: If you're in a Family Sharing group, purchases are charged to your personal Apple ID balance. If you don't have enough Apple ID balance to pay for the purchase, the remainder is charged to the family organizer's primary payment method.