I am a bit confused about gaining inspirations. I finally managed to work out that you get them based off of the dice matches. However, the example gives 2 different ways to match, but does not tell how to decide which to use. Who gets to decide how the matches occur?

Thanks,
Mike

Whoever controls the complication when it resolves, along with getting to narrate, decides how the inspirations match up, and even decides who gets the opposing side's Inspirations (if any). For example:

Winning side's dice: 6 3 1
Losing side's dice: 5 4

The player who controls the Complication when it resolves could match this up however he wants, but a good approach would be
1 - 4 = a 3 Inspiration for the losers
3 - 5 = a 2 Inspiration for the losers
6 - nothing = a 6 Inspiration for the winner

And if a couple of different players rolled on the losing side, the winner could give the 3 to one of them and the 2 to another, or both the 3 and the 2 to one of them.

(N.B. I'm obviously not Tony, but Tony's probably drowning in conventions stuff right now.)

I fully endorse this answer (including the drowning bit).