I haven’t really tried adding poems or songs to my stories, but I do write both, so let me see if I can help at all. 🙂
First things first, I agree that songs included in stories are really cool, and when I was reading The Ballad of Songbirds and Snakes, I’d make up a little tune in my head for each song. So yes, I think it’s a cool idea.
I think the first thing I’d consider is this: does the song add to the story? Putting songs in is fine, but it makes it special when the song actually has something to do with where the story is at or where it’s going. Sometimes you can even foreshadow with songs, or make so a reader finds out what happened previously in the story through songs. I saw that happen quite a few times in The Ballad. (I’ll just call it that to shorten it.) It wasn’t just some meaningless song that the author put in to make the story more unique or longer, it actually added to the story itself. So I’d first of all make sure that the songs you add would add more depth to the story. Adding a song that doesn’t have anything particular to do with it could still be okay, but it wouldn’t be the same.
Second, you have to remember that when you have a character write (or sing) a song in your story, the song has to fit with their personality. Do you know what I mean? Like the songs that Lucy Gray sand in The Ballad fit with her personality and what she’d gone through and was going through at the time of the song. So the song should fit with the character and their personality/what their going through.
I’m not really sure how to help with the actual writing the songs/poems part though. The only thing I can think of that would help get you started would simply be start writing! Think of a topic that you want a song/poem about and then try to write something out that fits with the theme. It may be rather difficult at first, but if you keep trying, it will almost certainly get better, even if it takes a while. And even if you’re not experienced in singing or writing music, you don’t really need to have an actual tune for the song, or at least nothing elaborate. The people reading won’t know what it sounds like anyway, so you really only need to be able to add some description of the general tune or style, or some such thing. It may be easier trying to write it with music, but if the tune isn’t coming and the words are, I wouldn’t bother with getting a perfect tune to go with it. If you want it but can’t get it quite how you want it, you can always go back and write it later or change it.
And one last thing that goes with the practicing part. Instead of writing out your songs/poems and not being able to decide it you think they’d fit with the story or are “good enough”, you could try giving them to a friend and seeing what they think. Even if they’re not a writer, they may be able to give you some advice on the song itself and if the theme is showing through.
Hope that helped!
Even the smallest person can change the course of the future. -JRR Tolkien