The Challenge description is pretty self-explanatory, but you can't get very far if none of your friends have any caddies for you to borrow.
It's worth noting that your caddies aren't automatically shared just by being friends with someone else playing PS Golf. You have to manually share a caddie for it to available to your friends.
In the Caddie Setup menu, switch to the caddie you want to share and press the View button (the new one with 2 squares on it). That caddie will now be available for your friends to use.Edit: More Info
So I've still been seeing "No friends are currently sharing any caddies" for a week, and I've figured out the problem. It deals with the Xbox One's new Friend vs. Follower system.In order to share caddies and play rival matches with someone, you have to mutually-follow each other.
It isn't enough to just follow someone who plays PS Golf - they also have to follow you back. Hopefully this is helpful info to others, as there really is no instruction on this in-game.