The first thing that's important to know is that Vietnam is not a signatory to the Berne Convention of 5 October 1961 Abolishing the Requirement of Legalisation for Foreign Public Documents.
Because of this, the US State Department Foreign Service in Vietnam (Embassy & Consulate) is FORBIDDEN from certifying any documents originating in the United States, be it a marriage license, birth certificate, diploma, degree, employment record or other document (continue reading #2 below for what CAN be accomplished at the Embassy or Consulate).
Documents originating in the United States can only be authenticated and utilized in one of two ways:
1. Submit in the United States through the Vietnam Foreign Services (Embassy or Consulate).
They will require that your document be:
A. Officially certified or notarized as a genuine original or copy at the level the document is generated (City or County Clerk or through an institution such as a University that conferred a degree).
B. Apostilled by the Secretary of State in the state where the document originated.
You will then submit that dossier to the Embassy or Consulate of Vietnam in the USA where they will provide both an official translation AND official certification stamps for both the document and the translation.
In effect, they will notarize the apostille as being genuine.
Even though they are not signatories to the Berne Convention, due to their placement in the United States they are uniquely qualified to certify the authenticity of state government apostilles.
Your dossier will then be entered electronically into the digital records system of the Vietnam Foreign Services and be available for use in Vietnam through the local Vietnam Foreign Services offices.
NOTE: they will also return your physical certified copy of your dossier to you.
This is the best method for people planning to seek employment in Vietnam.
For instance, if a person wants to be an English teacher and they have their dossier on file with the Vietnam Foreign Service, then they only have to give that information to prospective employers who can access everything they need in order to apply for a work permit.
2. Using the US Embassy & Consulate Notary Services
This particular method could conceivably be halted by any individual government in Vietnam, at the provincial or national level.
However, as crazy as this sounds (a total lack of logic) it continues to work for US citizens daily:
1. Bring your notarized copies of US documents to a notary appointment at the embassy or consulate.
(In my case, I had also obtained apostilles from the California Secretary of State, in addition to notarization/certification at the County Clerk level, but I have since seen many anecdotal reports of people completing this process without the state apostille and only having document notarization/certification within the previous 6 months.)
2. The US foreign service officer at the consulate or embassy will provide you with a template for a notarization.
It will be YOU who describes in your own handwriting the document(s).
It will be YOU who then swears to the authenticity of those documents.
The US foreign service officer will only notarize your signature and the fact that you swore to the authenticity of the documents.
That's the only thing that the US Foreign Service provides; a notarization of your signature.
After that, you take the dossier to the local office of the Vietnam Foreign Services.
That office will do two things:
A. Translate your documents officially and certify the translation.
B. Notarize that the signature of the US Foreign Service Officer is in fact genuine.
So nobody at either place actually certifies that your documents are genuine.
It's a notarization of your signature followed by a notarization of the signature of the US foreign service officer.
Logically, that should not suffice the legal requirements, especially when compared to what is done back in the United States by the Vietnam Foreign Services.
But in my case (with my marriage documents) and in many, many anecdotal reports in this forum, that completed dossier turns out to be acceptable to provincial governments and immigration offices and for work permit applications.
Some say it has to do with the mystical power of the notary stamp from the US foreign services and perhaps a misunderstanding of that stamp.
For whatever reason, that's what works for US citizens.
Other nationalities will have to chime in with what works for them.
Good luck!