When my daughter got her new computer, it seemed like an especially good time to create an account for her. But although, at 18, I think she's ready to manage her own music and balance her own allowance, she's surely not ready for unrestricted access to my credit card.
It took some searching around the iTunes support documents to find the solution, but there is one, and I share it with you now. You'll need a gift card or certificate to do it, so if you don't have one, buy one at a store or print one out from your own account. Be sure to log out of your account after.
Now, click the "Redeem" link in the iTunes store, enter the number on the gift card or certificate, and click "Redeem." Since you're not signed into an account, a sign-in screen will come up -- but it will have a "Create an Account" button off to one side. Click on that.
Enter the information you want to use to set up your child's account. You'll need an e-mail address, different than the one you used for your own account. What I did for my daughter, to give her a feeling of independence, was create a free Gmail account for her. I then went into the "Setting" for her Gmail account, clicked on "Forwarding and POP/IMAP," and set it to forward a copy of all her e-mails to my e-mail address. This way I get to see all her iTunes receipts, along with any other troublesome e-mail she receives.