If I control Willbreaker and my opponent attacks with something and I target it with Anointer of Champions, would I have to block their attacking creature? Do I gain control of it before blockers are declared? How does that work?

The Willbreaker's ability goes on the stack on top of the Anointer's and resolves first. When it resolves, you gain control of the creature, which causes the creature to be removed from combat. Then the Anointer's ability is countered on resolution, since its target is now illegal (it's no longer an attacking creature).