For a US passport holder, you can apply a Vietnam visa to stay up to 1 year with visa on arrival, or just 1 month with E-visa.
Firstly, you should know that US passport holder cannot enter Vietnam for a free visa. So, you need to apply for a visa before coming to Vietnam. The length of stay depends on the visa you choose:
E-visa: It allows you to stay a maximum of 30 days with a single entry. If you apply for E-visa, you can stay in Vietnam for duration of 30 days for a maximum.
Visa on arrival: You can apply for 1 month, 3 months, 6 months or 1 year staying for this type of visa. It allows you to enter and exit multiple times.