Small fountain pump - This one is super cheap but it works.
Decorative Rocks - crafts stores and the dollar store
Remote control outlet switchoptional
Instructions
Place the pump, especially the nozzle where you want the water to flow. I have mine off to the side but I think it would also look good in the middle.
Arrange the decorative rocks all around the bowl. Stack them up around the pump and cord to hide them from view.
Add water to just cover the rocks. You need enough water to fill the pump; if it is a submersible pump it can even cover the pump.
Then plug in the water fountain and enjoy it.
Video
Notes
Some pumps have a dial that lets you control the water flow. You can also consider purchasing a remote control outlet switch instead of unplugging and plugging the fountain in each time you want to run it.