Then first thing I do is I ask "how does this relate to my other sources and information I already have?", and the second thing I think is "how does this further refine my argument and change my perception of the information I know?"
My current research is to do with the composer Lou Harrison (not ancient, but the same thing applies to ancient documents and sources), so I'm going to use that as a guideline.
Part of my research involves researching Lou Harrison's interest in gamelan music and its influence on his music. He had a strong interest in Javanese and Balinese Gamelan music, and many people claim that he wrote a hybrid of western classical music and gamelan music.
Lou Harrison studied Gamelan for many years under various teachers, but before this he spent many years looking at Ethnomusicologist Colin McPhee's writing on Balinese gamelan music, doing many of McPhee's provided
This has led to me researching more into ethnomusicologist Colin McPhee (author of Music in Bali). A few things I learned: Colin McPhee was associated with one of Lou Harrison's composition teachers, and McPhee rarely ever played Gamelan music on the actual instrments. In determining the quality of McPhee's writings on Gamelan music, I was lucky to have access many other sources and gamelan music teachers to gain an understanding of the concepts, and look for western misconceptions in McPhee's book. I am also listening a lot of Gamelan music.
My conclusions from this were as follows: McPhee's approach to Balinese Gamelan is colonial/imperialist (us/them), and comes from a place of western thought. I can infer this because many of the examples, while aurally accurate, have front-weighted emphasis, and are noted in on a western staff with western rhythmic notation. Also, without having access to recordings of gamelan music it's pretty hard to learn. Also Colin McPhee has one hell of an ear.
From this I was under the impression that Harrison's Gamelan-inflected music prior to his formal study under Gamelan master Pak Cokro is full of misconceptions and mere inflections of gamelan music.
To show this I then analyzed some of Harrison's music I found a lot of Harrison's Gamelan-inflected music was just that: Western music written with small amounts of Gamelan inflections. His understanding was surface level, and I was able to understand why.
Conclusion: Colin McPhee's "Music in Bali" is a good source for my question. It refined my understanding Harrison's writing.This being said, McPhee's book would be a terrible source for someone studying Beethoven.
I hope this was useful. The older the source, the more difficult this process is. Determining how true a source is (like what I did with McPhee's book) is never easy, and it requires loads of knowledge. This is why historical research takes time.