Harry goes to Hogwarts, picks up where he left off with Ron and Hermione, an event is announced by Dumbledore and some new Dark Arts teacher is introduced who has some sort of physical or personality defect which becomes the fulcrum for an event later in the book.
Harry, Ron and Hermione do some sort of wacky stupid hijinks which may or may not involve a Slytherin member, sometimes going to the Library to figure it out, any combination of Harry, Ron and/or Hermione have some sort of personal conflict revolving around jealousy/insecurity (or multiple ones!) and then later sort out their differences through some event that brings them together again.
Most of the time, Voldemort happens at the end in some shape or form and then an event/plot twist happens towards the end that has been foreshadowed earlier (sometimes throughout the entire book). Dumbledore shows up to explain any inexplicable shit and reasserts how important/special Harry is, The End.
Lots of small variations here and there depending on the theme (secret book! escaped prisoner! wizard tournament! secret anti-death-eater society!) but all in all, there's certainly a rhythm to the series. lol, she even managed to cram in the dumbledore!exposition in the last book, ffs.