To do this, you'll need to find a purple fishing portal in the open zone and enter it. Once you're there, you'll immediately meet Big the Cat and be taught how to fish.
When you throw the rod, you'll press
when you get a bite.
A red circle appears around it, and all you need to do is press
(or
) at the right time, so that the white circle lands in it.
It's easier to see what's going on:
The controls are different, but the principle remains exactly the same: press at the right time.