The hangman's noose has been suggested for the task. After the lines are tied off, if you pull them in opposite directions they will cinch up the ends of the leather strip and form a longitudinal concavity, a perfect pouch. If you can find, or cut, a pouch that is a little more oval in shape, so much the better. Rocks are the most common sling ammo, and they are usually plentiful. Once you get the hang of it, you can move to lighter ammo that travels faster and farther.
Rocks are also dangerous however.
If you slip up it is easy to send a your missle in the wrong direction, so try to find a place where an accidental mis-release won't hurt people, animals, or property. I have found an interesting alternative ammunition that is pretty harmless no matter how hard it is thrown. I am lucky enough to have access to a syringe and needle as my wife is a nurse. I took some old but otherwise un-torn tennis balls and injected them with water. They take about 45ccs, and that makes them heavy enough to be thrown, but they decelerate rapidly.