how do you actually get to know an artist or album the way you know a show after watching it so that you can talk about it without feeling like you're faking it?

Military taught me to just dive in headfirst so thats what I did with music. Pick one album you actually like and just live with it for a week - play it while doing dishes, knitting, whatever. You'll start noticing little things like how the drums change or which guitar parts you hum along to. Once you can hum the bassline youre basically an expert on that record and can talk about it way better than someone who just knows the singles.

Headphones, quality ones. Pick from different styles like Miles Davis for jazz, pink Floyd for rock, black sabbath for heavy metal, Kenny Chesney for country, Supremes for motown, .B.B. King for blues, Bee Gees for disco, Harry Chapin for easy listening and Tchaikovsky for classical. I'm listing some of my favorites from these styles but there's so much more than that. I was a musician and also had a DJ service for years and I lose myself in music. I have specific things that I could suggest if you like.

You listen to the artist a lot. Music is poetic, so you have to listen to songs enough to pick out meaning. Sometimes the first thing you notice isn't exactly what the artist intends. It can also help to read up on an artist. Understand where they are from, how they live, their struggles or lack of, their inspiration, and so on. It adds insight into the music. Oddly, I was better at this before the Internet. I thrived on magazines, interviews, album booklets, etc.

The first step is just to start by paying attention to what you like. Look up the musicians (like on Wikipedia, for example). From there you can find out what genre they're in (as well as things like the musician's history, where they fit in in the broader context of music, who they were influenced by, who influenced them, etc... but at the very least find out what genre they are generally associated with). From there you can look up the genre, find other musicians working in that genre. There are many resources online for exploring music genres from online lists, wikipedia pages, and playlists on steaming services like Apple Music and Spotify. Listen to more musicians in the same genre and figure out if you like any of them. Pay attention to the similarities between different artists in the same genre. Pay attention to what they're doing differently. To explore outside of a given genre, you can also learn about who influenced your favorite musicians and who was influenced by them. I also recommend seeking out reviews of the music you like. In addition to giving you more ways to appreciate the music (or, at least, another perspective on it whether you agree with it or not), reviews will often help to contextualize the music further in terms of what other musicians it sounds like or might be influenced by. Also, this may or may not go without saying, but if you like a piece of music, listen to more music from the same artist. If you like a single song, listen to the album its on. If you like an album, listen to the album the artist made right before it, or right after it. To give a personal example: When I was first developing my music taste, I got into Queen of the back of Bohemian Rhapsody. I listened to the rest of the album A Night at the Opera which I loved. I then started exploring more of Queen's albums, and found that the album Queen II had a lot of what I liked about A Night at the Opera. The little review blurb on iTunes described my favorite tracks on Queen II as "Prog Rock." From there I looked up Prog Rock and discovered one of my favorite genres. I found a list of "the top 30 Prog Rock Albums of All Time" and started listening to albums from that list, and then to more albums from those artists, and so on. The same thing happened with other genres, just branching out from starting points. So, the tl;dr is: pay attention to what you like, listen actively, look stuff up, follow connections to find more music, repeat.

As far as artists go, look for some background. Articles, interviews, maybe vlogs if they're still small-time. With albums, I've been slowly getting better at identifying the elements of songs I like, but still struggle at articulating why it appeals to me.