How do you recruit the best person for a job?

I came across this video thanks to a brilliant article written by Rob Schwartz on Forbes.

I think recruitment is an industry that is ripe for disruption. These examples are a growing testament to the need for showcasing your ability to do a job ... before you actually do a job.

If you want to hire the best person to replace you in your current job ... how would you test him or her? What would they have to showcase?