Step 3: Mount it
I drilled pilot holes and then just screwed the mirror hangers in. And voila! The basket was mounted!
When I marked where the hangers should go I didn't check to make sure there was actually an open spot in basket. As a result the hangers bumped right into part of the basket. So take this into account when you figure out where exactly to place the hangers.
Also, I'd recommend placing the hangers between wires of the basket, that will make it much harder for the basket to slide out if it were bumped.