I guess my scope basically surrounds the Cold War. E.G. it's generally well-understood that the U.S. played a role in the training of the Mujahedeen, yes? But how do we know that, aside from American weapons (notably anti-aircraft weaponry) being used by them. Sometimes, the governments of countries outright do it openly.
But, if I'm trying to find out, as a random guy, if Soviet advisors/volunteers were sent to Vietnam, could I somehow contact the Russian government and ask "Hey, can I peruse your old top-secret files?" - Obviously I'm kidding, but what route would you go through.
If you're asking, how do write a history of secret things, the answer is:
Some of these things, as you note, are "open secrets" even at the time, and a lot of documentation was done by journalists with various levels of confidential sources.
Some of them become the subject of official inquiries and official testimonies get written about them (this is how we know so much about CIA stuff prior to the 1970s, for example — the Church Committee dug quite a lot of that out).
In some countries, there are Freedom of Information laws that allow for the declassification of secrets under various conditions. In the USA, the Freedom of Information Act can be used to get a lot of information about once-secret things. Sometimes things are still blacked out, but there are techniques to get around that (like triangulating from multiple sources). Sometimes governments just release these files unbidden (Russia, for example, released a lot of files about their World War II atomic espionage in the 1990s).
Sometimes historical participants will tell you things, either on or off the record, that are still technically secret. I have a colleague who works on the Israeli nuclear program, which officially is unacknowledged by Israel, and he has gotten a number of former Israeli officials to give him information about it under the terms that he won't release his interviews with them until after they die. Such people sometimes write memoirs, give interviews with journalists, and so on, that spill some of the beans, and you can collect and compare these to build up a larger picture.
There's no magic involved. There are always some things that one knows are out there but denied from one. You keep at it.
I’ve actually spent the past year study the Mujahedeen so I can speak a bit to that example.
Besides the obvious proof of the Stinger missile, declassified documents from State openly talk about sending the Mujahedeen cash payments via Pakistan. Most aid went through that route, but CIA chiefs in Pakistan also attest to cash payments made directly to Mujahedeen leaders like Massoud. (Haqqani also received payments from the CIA but I only know the hard numbers for Massoud).
These personal anecdotes are another key source, though not always reliable. This one directly relates to your Vietnam example: When Ahmed Massoud complained about Pakistan’s support for the Taliban, his primary evidence was Pakistani military officers being taken prisoner by his men after skirmishes with the Taliban. It’s always possible for sources to embellish or lie, but the plausible deniability most states exercise when dealing with covert aid doesn’t leave room for many other options.
It’s possible that the records you’re looking for are actually available at some museum or public library, but I doubt they would open the archive for, as you say, a random guy. Even in the U.S., where FOIA requests can be made for classified material, you still need to show some credentials or credible research in many cases. Otherwise, you’d need to rely on secondary sources and eyewitness accounts.