you’re right about the keyframe, but it’s a bit more complicated than that.
First, you have to use Blender 2.25 (which I guess you didn’t since you didn’t complain about the file not working ).
Now, if you select the ball and go to the Constraint window (click on the Icon that looks like two chain links), you will see 6 constraints:
Each pair of Loc and Rot constraints are the different parents.
You will also nottice that each constraint has an Influence slidder next to it.
This value determines how much a constraint will affect the object.
A value of 1 means total influence, a value of 0 means no influence.
Now, switch the text window on the right to an IPO window (Shift-F6)
By clicking on the Edit IPO next to each Influence slider, you will see that the IPO curve on screen changes to show the one attached to this particular constrant.
By playing with the IPOs and by using Constant type curves (Tkey to change the types), you can switch between the different parents.
I hope that’s more clear.