Before your child goes to China:
1. Install Skype (download here). It does not matter what computer it is installed on.
2. After installing Skype, you will be prompted to register for a new account. (Of course, if your child already has one, you can skip this step).
3. Sign in to Skype
4. After signing in, click on the "View account" button
5. Click on "Buy more credit" ($10 goes a very, very long way. Skype only charges $0.021 to $0.024 per minute while redirecting to China)
6. Click on the "Online number" tab, then proceed to purchase an online number.
7. Make note of this number.
8. Log out of Skype.
After your child arrives in China and has obtained a cell phone:
1. Sign in to Skype
2. After signing in, click on the "View account" button
3. Click on the "Call forwarding" tab
4. Enable call forwarding
5. Enter your child's Chinese cell phone number in the "Your calls will be forwarded to" field (don't forget to include +86)
6. Log out of Skype.
After this process has been completed, you can call the "online number" which you have purchased from Skype. When you call this number, it will check if your child's account is logged in to Skype. If it is, then it will automatically connect you to them through the Skype account. If not, then you will be automatically connected to his or her Chinese cellphone.
This is a convenient solution because no calling cards are required. Instead of dialing an 800 number and entering in long codes, you can just dial a local number and be billed for a normal local call (plus $0.02/min deducted from the Skype credit). Also, this way several family members can easily contact your child without needing to share or purchase their own calling cards.