How It All Goes Down
The Complete Tales take place across two separate books: Winnie-the-Pooh and The House at Pooh Corner. In general, all the actions take place within an episodic narrative structure; that means that there isn't really a plot that continues throughout the whole book. Instead, each chapter is a story in its own right and can be read separately from the others. True, a few stories reference events that took place in ones that came before, but none are really essential to your understanding of the episode at hand. It's like watching old sitcoms—you can pretty much pick up wherever you want.
But like any series, there is a loose overarching plot point: Christopher Robin grows up. The two books were published two years apart, and Christopher Robin's age more or less follows that time span.
And that's all we'll give you because IOHO, it's just not right to briefly summarize Pooh: this guy's too charming for that.