Assuming there's no destructive civil war/issue with disobedience by the state to the military clique in Washington, it'd likely involve whacking Canada over the head and dragging it off at some point while Britain is distracted; making it more of an ally of convenience to Hitler than anything. The US ultimately has few interests in Europe and little to gain by actually sending military forces in that direction, and unlike Germany, Italy, and Japan actually had essentially controlling economic interests in those areas an otherwise "second-string" power might want to break into via military force (Cuban Sugar, Mexican Oil and infrastructure, Central America is basically owned by American companies at this point). America simply lacks the same kind of motive for military expansion/autotarky that the Axis in our timeline did; its economic woes come from a lack of markets.
I WOULD expect to see a massive increase in arms sales to Germany and Japan though, since any Facist regime is likely going to be tied closely to business interests who want to get their lagging industry back up off the ground and make profit. Looking at the bundles they made during WWI by providing weapons while other provided blood, I could see Japanese troops paroling the stretches of China or into Siberia in legions of American built jeeps, running on American petrol, and shooting guns with American bullets, paid for with wealth ripped from conquered lands, while the US scoops up abandoned British and French territories/economic interests in the new world under a twisted version of the Monroe Doctrine/Manifest Destiny. As for the political control of Latin America... let the local dictators handle things and keep their fancy suits. So long as they let the CIA and American multi-nationals strip all your natural resources.