My fiance was born in USA but has lived in Canada for 10 years and now we want to move to Arizona. How do we?

You fiance is fine moving to an living in the United States if she was born there. She will need a passport to travel to the United States -- either her US one or (if she also has Canadian citizenship) her Canadian passport and her (US) birth certificate. Children born to a US partner outside the United States do not automatically receive US citizenship and can not remain in the US. If you haven't already done so, you'll need to register your children's birth abroad at the nearest US embassy or consulate. This should have been done immediately after birth and if not, it may be a somewhat lengthy process. With this, your children will receive US citizenship cards. Children 16 or over will need passports to enter the US as will any child flying. So, you'll probably want them to have either Canadian or US passports. I do not understand "we want to move" and " would still be working in Canada." You, as a Canadian citizen may visit the United States for six months. In order to stay longer or work, you require a green card. In order to get one, your (American) wife will need to sponsor you. She'll need a solid job history, financial statements showing she can support you, a permanent residence, etc. and then she'll need to apply for a green card for you. The process may take a year or more. You will need to undergo background checks, interviews, etc. I don't understand how you could be working in Canada while living in Arizona. That makes no sense. If you are physically in the United States, any work you do their is working in the United States. It doesn't matter if it is online, telephones, or morse-code... you must have a green card, pay US taxes, etc.