Mary Poppins (Julie Andrews)’s Timeline and Summary

Mary arrives on a flying umbrella, miraculously responding to the children's ad for a kind nanny—which was torn up and thrown in the fireplace by Mr. Banks.
She immediately starts using magic to teach the children lessons about life, and helps them clean up their nursery by making all the objects and toys move on their own.
Then, teaming up with Bert, she leads them into an animated fantasy world, contained inside a chalk drawing, in which they go on a horse race, and perform musical numbers.
Next, she takes the children to see her Uncle Albert, an old dude who floats when he laughs. Pretty soon, everybody's floating (though they get back down).
Then, after the whole tuppence fiasco at the bank, Mary chases after the children after they've been sucked up a chimney.
The "Step In Time" musical number ensues.
Finally—once Mr. Banks gets fired, becomes a changed, man, and goes to fly a kite with his kids—Mary leaves, flying away on her umbrella.