And what is the best way to do that? Should I get them their own credit card? Add them as a user to mine?
You are on to the right track. I was able to secure a junior credit card at just age 17 with my father as a cosigner. My credit quickly escalated over the following 2 years to the point where I was receiving multiple credit offers. Get them a card in their name, with you as a cosigner, and monitor the activity (at least initially). Once they build sufficient credit, they can get their own card.