If you've already been evacuated to a US Navy ship in the South China Sea, then you're on your way to the US. You'll be taken to a resettlement camp. Many were taken to Camp Pendleton, CA. They received limited training on acclimation to US life, language, etc and assistance in setting up their life and applying for social services. Have you heard of Little Saigon (Saigon nhỏ) in California? If you look at a map, you'll notice that it's not far from Camp Pendleton, a US Marine base. They moved 50 miles up the coast, and settled there. They sought out odd jobs, usually much below their level of training. A pilot would become a maintenance man at an airfield and so on. At some point women found success in nail salons. Others followed suit. (For Cambodian refugees, it was donut shops).

The refugee experience varied depending on which wave you were in. The scenario you described is first wave, the immediate aftermath of the fall of Saigon. For people in the later 1970s or 1980s escaping on boats into the South China Sea, the experience was much different, and much less sure. Thai pirates cruelly preyed on these boats. Representative of this is a scene in the documentary Oh, Saigon. This young woman's boat of refugees was taken by the pirates who raped her. Many others were killed. They could be rejected by potential host nations, or sent into small detention camps like those in Hong Kong. It was a terrible human crisis. Not to mention that the Vietnamese government (the Socialist Republic of Vietnam) made them pay exorbitant fees to get on the boats. Your hypothetical character would face a much easier path.

If you were part of the 'third wave' in the late 1980s and 1990s, the first being right after the fall of Saigon and the second being the 'boat people' crisis, then you faced a much different path. Mainly you sought coverage in the ODP (orderly departure program). You needed to qualify (say that you served in the Republic of Vietnam army, police, government at some level and the SVN gov agreed that you could leave) and then find a sponsor in the US. Many people connected with old buddies in the US military, perhaps an advisor in their unit. Others had family in the US from the first and second waves of Vietnamese migration. Others depended on volunteers, like church groups.