The series is, as a format, one of the holy grails of commercial fiction. It lets you lock in a readership for consecutive books, allows for a fandom, and of course gives you an excuse to push for a multi-book deal with a publisher.
This explains pretty succinctly why it’s done so poorly so frequently – as the saying goes, when dumb money follows smart money the party’s over. In this case, when dumb writers follow smart writers, we see a proliferation of half-formed series dragged out of enough material to fill maybe half a book. That in mind, let us save ourselves and our readers from the obvious pitfalls, shall we?
The biggest and most frequent mistake I see is what I’m calling Series Opener Syndrome. That is, using the first book as exposition, a cliffhanger, and a big middle finger to anyone waiting for a story to show up. This is a response (not to be confused with a solution) to a major problem – a series frequently requires a big world, and a big world demands a lot of exposition. The temptation to get all your cards on the table so the reader knows what they’re getting into is an understandable one, but the problem you run into is that you’ve essentially written one very long, very dull sales pitch for books that frequently don’t even exist yet.
The most common way to fix this, and certainly the easiest to pull off, is to make each book in the series a story rather than a story element with its own plot arc. Yes, the larger series will almost always constitute a story arc unto itself, but each book should also be a story. Someone should be able to read one book and enjoy it on its own merits, and this is doubly true for the first one; the first book is the one you’re using to establish how enjoyable your writing is for new readers. That doesn’t mean you have to drop the exposition, just that you need to have a very distinctive, enjoyable series of occurrences that happen to contain exposition, not exposition that fills in story where it needs to.
The easy way to do this, and in my opinion the most effective, is what we might, as a slap in the face to three thousand years of literary history, call the Harry Potter Method. That is, have an overarching story like the rise/pursuit of Voldemort that underlies the entire series. Give the series a goal, something that it’s doing over the course of the entire thing. But! Also include a small intermediate goal in each book that is vaguely related to the larger story but nonetheless stands alone and can be dealt with and addressed over the course of a single book. Harry Potter and the Sorcerer’s Stone had the… well, Sorcerer’s Stone. Harry Potter and the Chamber of Secrets had, and I hope you’re seeing a pattern here, the Chamber of Secrets, and so on. Each of these had something to do with Voldemort, but they also had distinct arcs of their own.
Failing that, if you’re looking to be a bit more avant garde, you can simply omit the traditional plot arc entirely. You’ll see this frequently with journey fiction, but it need not be journey to work. By simply having your characters move evenly towards their eventual goal book to book, giving exposition, conflict, character development, and so on along the way, you escape the narrative structure and in so doing prevent the issue of Series Opener Syndrome by spreading your exposition, your conflicts, your climaxes, and so forth across the books, having no particular section of rising action and thus not needing to have an entire book made up of it.
This last is a difficult thing to pull off, though you see something similar to it in Lord of the Rings and the early Dark Tower books (note that both are journey fiction), and when it works it really, really works.
In any case, be very certain not to allow the first book to be simply a lead-up to the latter books, nor for that matter to let any book become the red-headed stepchild that merely exists in service to its fellows and has nothing of its own to add. Make each and every one a good book in its own right, or you’ll have readers go no further than the weakest link.