To start off with, you should be able to ride decently without flailing your arms about. Then you practice by what we call "noodling": you lean forward and let your arms hang as close to the ground as possible. Then you put down pringles cans, or milk cartons, and scoop them up as you go by. Pop bottles work well too, as they have a nice little lid to grab. Juggling clubs are very ideal, if you stand them up on their end. However, if you're juggling as you ride and you drop one, it's doubtful that it will land like that, so you might want to practice picking up clubs on their sides. :)
The method we use for getting really low things like clubs or bean bags involves kind of a still stand. We ride up to the object and stop with our pedals horizontal, in the jump position. Then lean forward and bend way over, pick up the object, and as you start to fall forward, resume pedaling. Tammy can touch the ground on her uni with her seat at the normal height for her.
Here's Tammy, picking up a pop bottle.