How exactly does multiclassing work in Pathfinder? Has anything been changed compared to the 3.5?
Two answers: 1) We don't know, the rules were not included. 2) By default, use 3.5 rules for how to multiclass.
What does the change in the favored class ability mean for multiclassing?
It means there is no XP penalty for multiclassing, ever. And it means you'll get a favored class bonus (assuming you have one) only some of the time. So if you're an Elven Wizard/Rogue, you'd probably pick Wizard as your favored class, and get the bonuses only when you take Wizard. If you were an elven Wizard/Ranger, you'd have to pick which of those you think you'll take more levels in (or more levels sooner, or whatever other reason you like) and pick one.
[Note: Favored class specifics are rumored to be changing by the final edition, but should follow what I just said above.]