From August 26th 2016, 1-year multiple entry Vietnam Visa is the only visa available for U.S. passport holders. 1 month, 3 month, 6 month and single entry visas no longer exist.
Furthermore, the maximum duration for a single stay is 90 days, meaning you can’t stay in Vietnam for more than 3 months at a time, and have to leave the country and return for another 3 months of stay.
There are 2 ways to obtain 1 year multiple entry Vietnam visa for U.S. passport holders.

Option 1: Applying at Vietnam Embassy or Consulate
You can apply for 1 year multiple entry Vietnam Visa at Vietnam Embassy in Washing DC, or at one of three Vietnam Consulates in New York, Houston, or San Francisco.

Processing time: 5-7 working days (not including mailing time)

Total fee: US$220

You can find the bilingual application form on Vietnam Embassy website. After filling out the required information, you need to deliver or mail it to the respective Vietnam Embassy/Consulate attached with service fee and relevant documents (including original passport and 2 passport-sized photos).

Option 2: Applying for Vietnam Visa on Arrival
This is considered to be the fastest and most hassle-free method so far to apply for Vietnam visa. You can submit an online application directly here. After filling out a very simple online form (which is also available for download in Word format) and completing your payment, you will receive a visa approval letter via email. All you need to do later is to print out the letter and prepare original passport, 2 passport sized photos and stamping fee for getting visa stamp at one of three Vietnam’s international airports. The service fee for the visa approval letter is US$50, and the visa stamping fee is US$135 (which you will only pay in cash upon arrival)

Processing time: 2 working days for regular processing

Total fee: US$185 (US$50 visa approval letter fee + US$135 stamping fee)

Shorter and more simple online application form