Usually I read things in chronological order. It makes more immediate sense to me to do so. In certain cases this isn’t what the author intended (The Chronicles of Narnia) and in some cases it isn’t what works best (the Star Wars movies). But usually the creators of the works are on the same page, that a linear progression of time is the most logical way to tell a story.
The second installment of a story has to do two things, and this can be tricky: it has to continue the story from where it left off, and it has to catch up the new listeners just tuning in. Some books try to do this with a little author’s note at the beginning — sort of a “previously on” like in tv shows. This might work or it might not, depending on the mood of the overall story; it’ll probably work better if it’s humorous, or maybe that’s just me. Some books try to do it with carefully rationed infodumps parceled throughout the beginning chapters, little “oh by the way”s and such. And other books just allude to the the goings-on of the first part of the story, and only make them plain as they become relevant to the next part of the story. I think I like the third option best, but I’m finding it a little tricky.
There were seven Harry Potter books, and six of them had to catch up new readers at the beginning. JKR did this with neat little infodumps. There were — are? — God knows how many Artemis Fowl books, and again, most of them had some sort of exposition near the beginning, if I remember correctly. Since I’m planning on the Iron Gentry series being kind of a big sprawling series, I should probably reread those books just to study their techniques. But there are two books in particular that I’ve reread that are, I think, probably the best examples of sequel handling I’ve ever come across.
The Oracle Betrayed series by Catherine Fisher consists of three books: The Oracle (formerly The Oracle Betrayed), The Archon (formerly The Sphere of Secrets), and The Scarab (formerly The Day of the Scarab). (I don’t know why the titles changed. The covers did too, but that’s a less mysterious thing.) I first encountered these books in the children’s section of my public library, I think when I was in middle school. But I started with The Archon, instead of The Oracle.
In a nutshell, public libraries: they had a copy of the first book, but someone else was borrowing it. I was too curious to wait — I read the blurb on the back and promptly checked out books two and three. And so I was introduced to the world of the Oracle. It felt seamless. I knew I wasn’t reading the first introduction of these characters, but Fisher’s writing displayed them like old friends getting reacquainted. It helped that time had passed in-universe, so that every reader had catching up to do and not just the newcomers. (A handy trick, and one that I’m using in my own work.) But more than that, it wasn’t a whole bucket of backstory being dumped into my head. It was gradual and subtle and dang, but it made me fall in love with the characters. The Jackal is still one of my favorite antihero/badguy mashups ever. So, a rousing success, and a great example that I’m trying to learn from. I’m off to reread it again.