Monday I spoke at a local school for a bunch of art students and a lot of business stuff came up about selling online. There are a lot of great creative kids out there who would like to sell the things they make. Personally I think it can be a very valuable learning experience for a kid to start up their own little business. So if you have a creative child who wants to try to sell their work, give them a shot at it but realize it is going to be work for you as well as them.

Legally children under 18 can't enter into legal contracts so as the parent you are ultimately responsible for any online accounts, bank accounts and so forth. This means that you're going to have to do a good bit of work, the younger they are the more work you'll have to help them with. Research with them local rules for businesses, help them with the books, you'll have to accompany them to the bank to set up an account for them (most states don't allow kids under 18 to have a bank account on their own), and teach them how to manage their money.

Most selling venues online require a credit card to set it up (and paypal prefers you have one on file). Since I don't think most kids should have access to a real credit card instead of using your own consider using a prepaid card or setting up a checking account with your child that has a debit card with a credit card logo.

On the subject of money I think you should put rules down at first about how their money must be spent or saved. A portion should be for personal spending, a portion goes back into the business, a portion to savings, and a portion to charity (let them pick whch ones, it'll mean more to them). What the proportions should be will constantly change depending on their age and how much the business is making. For a younger child (say 9-10 years old) an even 1/4 split between them would be simplest to handle but as they get older they may want more money to go into growing the business or going to college savings. Discuss it with them every few months. As your child gets closer to 18 you need to back off and let them make more of the decisions to prepare them for when they'll be on their own.

Links:
Etsy Guidelines for Sellers
Forbes article on Raising an Entrepreneur
These Kids Mean Business Documentary (aired on PBS)
Kids and Money Books on Amazon