Your wife will need a visa to stay for longer than six months. It looks like you should start here for information: https://www.gov.uk/join-family-in-uk. The visa described on that page is rather costly: £956.
It looks like she could also go to the UK without a visa, and apply after she arrives. That process is described here: https://www.gov.uk/remain-in-uk-family. This is less expensive: £649 if you apply by post.
Your son is quite likely a British citizen, depending on your citizenship status and possibly on the reason you were in the US when he was born. If your son is a British citizen, you should apply for a UK passport for him. He will then need no other paperwork to live in the UK. The passport fee is far lower than the visa fees (roughly £50 to £100 depending on your son's age and a couple of other factors; see https://www.gov.uk/passport-fees).
To check your son's citizenship, visit this site and enter your son's information: https://www.gov.uk/check-british-citizen.
As US citizens, your wife and son will not need any paperwork to return to the US.