I went through this a couple of years ago with my kids.
I added my daughter (now 22) to a Chase card. I talked to Chase and they said the ONLY way the credit card would impact her credit score was to have her fill out a special form with her social security number. She now has a better credit score than me (>800) and will probably be buying a house this fall. ... I taught her to be a miser; she now gets great joy out of using 'coups' (coupons).

I added my son (now 19) to a USAA credit card when he was 16 or 17. I also had to have him sign a form that included his social security number. I'm not worried about him; he's getting a good financial education from both me and the real world. I don't know what his credit score is; no need to check on it since he doesn't need any credit.