Broadly speaking, the answer is a) having a very good knowledge of the music of an era in a particular style, and b) being aware of your biases, doing your best to correct for errors, having a clear basic framework of what the various factors involved in an album changing the course of a genre are.

Obviously, my particular opinion about a particular album is not going to be shared by everybody, but the nature of musical aesthetics is that there aren't objective truths - music is, after all, just a pile of noises arranged together. Some of those arrangements might be more aesthetically pleasing to my ears, and I might appreciate them more - but if that's the case, it's not just that the music is better; better is a value judgement that means nothing without context - what exactly is it better at?

Usually, if you analyse what is meant by music being 'good' or 'better', etc, there's an implicit (or explicit) task that music is meant to do, culturally. For example, Rolling Stone picked Jimi Hendrix as #1 in their greatest guitar player of all time list, and justified it as being because no other guitar player summed up the 1960s with their playing quite as well as Hendrix did. What's fascinating about this is that Rolling Stone did this list in the 21st century, with an audience that often wasn't born in the 1960s and won't really care about the 1960s; it reflects a (baby boomerish) model of aesthetics that prioritises certain musical characteristics present in some music (Jimi Hendrix, obviously), and not in others (Yngwie Malmsteen, say, is technically a superior guitarist to Hendrix in terms of the ability to play lots of notes quickly, but that's not what Rolling Stone are going for, because their aesthetics aren't about technical proficiency beyond a certain point - there's also punk guitarists on that list whose solos are simple indeed).

Anyway, after you read a lot of stuff about music, and about how one album might have influenced a particular aesthetic (say, a genre), what becomes clear is that a cultural industry like music has many people of influence, from the musicians themselves to the culture around the musicians, to the industry around the musicians to the fans and the way they react to the music.

Obviously, the music doesn't get made unless you have musicians writing and playing the music. But they're only writing and playing that particular music because they've come from a particular culture that prioritises this over that, that has heard this bit of music and not heard that other bit of music. Paul McCartney wrote and played a role in arranging the Beatles' 'Helter Skelter', because he had heard 'I Can See For Miles' described as being particularly heavy, and had then heard it and been a bit disappointed; 'Helter Skelter' was McCartney's attempt to get onto record something closer to the 'heavy' he heard in his head. Without 'I Can See For Miles', 'Helter Skelter' would likely not exist. But also, without a culture where at least some saw some value in the idea of 'heavy' in music, McCartney wouldn't have bothered making 'Helter Skelter'. And remember that the Beatles lived in a capitalist society where they were a premium capitalist product, effectively - the decision to release and promote 'Helter Skelter' on the album The Beatles (The White Album) was a decision ultimately made by multinational corporations, because The Beatles, despite their weirdnesses, were a reliable product in terms of sales. Radio stations played the Beatles not because The Beatles (The White Album) was a fantastic work of art that every needed to hear, but because radio station deejays had a lot of interest from fans, which translated into it being commercially advantageous for those deejays to play the Beatles - even something as heavy as 'Helter Skelter', because it resulted (seemingly) in more ears hearing the ads played after the Beatles song. Press outlets like newspapers and specialty magazines covered the Beatles in the belief that their actions were news that people wanted to read about. Finally, it was a reliable product in terms of sales because there was a fan culture that had developed around the Beatles which showed continued loyalty to the Beatles, and a sense in wider pop culture, by 1968, that the Beatles' cultural products were artistic and interesting, and that they reflected something about the times the Beatles lived in.

And in terms of discussing that historically, well, there's records of much of this. With the Beatles in particular, who are very, very well profiled, with an enormous amount of books written about them: you can find out what Paul McCartney said at the time and what he said later about why 'Helter Skelter' was the way it was (there's a 1997 book called Many Years From Now where McCartney). You can identify where The Beatles fit into the corporate history of EMI as a record label, to get a sense of how they would have taken The Beatles and how much pressure there was on the Beatles at the time to produce hits (for example, more recently, if Coldplay's X+Y album really tanked, it might have bankrupted EMI at the time, because they were financially on fairly insecure footing at this time, and it's fairly clear that this played a role in the fairly safe direction that X+Y eventually took) You can read cultural analyses of what 'Helter Skelter' might have meant at the time, and how that meaning has changed over time (Ian McDonald's book Revolution In The Head discusses the original innocent fairground meaning of 'Helter Skelter' and how the song acquired new meanings thanks to a murderous cult leader, Charles Manson, who heard other things in the song). You can look at data about how popular the album The Beatles was - you can look at where it was in the charts in different countries, and how that compared to previous Beatles records. You can look at how the press covered the record at the time, and what people said about it, and you can get a sense of where those writers were coming from especially if you know more of their writing and what they usually like. There's also some oral histories of Beatles fandom around, and you can get something of a sense of how different groups of fans perceived a song like 'Helter Skelter' and what they got out of it compared to what was intended.

But broadly speaking, pop music is quite a rich tapestry that has been written about a lot, both at the time, and in later periods, if not necessarily by academic historians (though sometimes they have been written about by academic historians). With an understanding of what usually happens to cause a shift in the direction of a genre, you can get a sense of where a particular album fits - you can look at the shift between one album and the next in other groups - The Beatles was obviously part of a post-psychedelic 'back to the roots' phenomenon of 1968.

Because the Beatles were enormously popular, and The Beatles sold well, they provided space for other groups (whose record companies gave them shorter leashes) to also try the 'back to the roots' thing (which the Beatles didn't start - The Band's Music From Big Pink was a big influence on a few people, including the Beatles, who quoted 'The Weight' during a live-on-TV perform of 'Hey Jude' earlier in 1968). Creedence Clearwater Revival had several hits in 1969 in a rootsy style, Crosby Stills & Nash released their first largely-acoustic-based album, Elvis did the From Elvis In Memphis album, seen as a return to roots. The Grateful Dead in 1970 released two acoustic song-based albums Workingman's Dead and American Beauty, which moved away from their trademark psychedelic jams. Neil Young moved from his quite ornate studio-focused self-titled album in 1968 to a back-to-the-roots approach on Everybody Knows This Is Nowhere. To some extent, the existence of the Beatles' 'back-to-the-roots' vibe played a big influence on many of these artists, and on some you can see a direct link - Crosby Stills and Nash covered The Beatles' 'Blackbird' from The Beatles, while Elvis covered 'Hey Jude' (a hit single recorded during The Beatles sessions). Elsewhere it's often in what's closer to music theory where the links can be seen, in analysing things like chord progressions or singing styles; I think John Fogerty's 'Wrote A Song For Everyone' (from their 1969 album Bayou Country is a fairly clear pastiche to The Band's Music From Big Pink, and in particular 'The Weight', and you can hear it in the similarities between the half-time drum beats, the way Fogerty pitches his voice, and the chords used (and a few other things). This is where the good broad knowledge of the music of the era comes in handy - it gives you a better sense of what's a band sounding like themselves, what's specifically influence, and what's part of the Zeitgeist in that era musically.

You can read me using aspects of these kinds of approaches answering the question of whether 'Helter Skelter' was a big influence on heavy metal (I didn't think so) and exactly how influential Sgt Peppers was.

There's definitely room for discussion here, but for an example of great ways to cover the history of pop music, have a stroll through /u/hillsonghoods' flair profile.