Charlie writes, "I am a naturalized US citizen and have one US born child, but I also have two children from my first marriage to a woman who still lives in my native country and is raising the teens there. I think it will be great if they can have American passports allowing them to study, work, and live here. What do I have to do?"
The simplest option for you would be to convince your current wife and ex-wife to let you allow to bring your children to America on green cards (it will be easy for you to sponsor your minor kids and they will have a very brief processing time). After they live with you, then, you can file USCIS Form N600 for their certificates of citizenship (all these steps must happen before they turn 18) that can be used to apply for passports. Once they become US citizens, they can live anywhere they want. By the way, if they are close to 18 and not all steps can be completed before the eighteenth birthday, they will simply have to live in America for five years and file USCIS Form N400 for naturalization (so it will take a lot longer and in the meantime they may only be able to visit their mother but would largely live in America with you).
The second option for you would be to convince your current wife to move with you to your native country. You will also need to convince your wife and ex-wife to let your children move in with you under your legal custody. Then you can apply on USCIS Form N600K for their certificates of citizenship, yet again, before their 18th birthday. Once they become citizens, they can obviously live anywhere in the world.