I have heard that a pump will keep the water clear. How big should my pump be? Must it run all the time?
A pump will never keep the water clear. A pump moves water and provides oxygen for the fish if you feed them and the pond is overpopulated. If you have a natural ecosystem there will be no overpopulation and therefore you will not need any pump if you don't wish to have one. Most folks like them because we all like the sound of moving water and waterfalls.
You ned a pump that circulates all the water once per hour. Most people run the pump all the time, but it is not necessary at all. You can run the pump on a timer or when you are outside to enjoy your waterfall.
No pump has to be turned on all the time unless you feed your fish or have koi.
And if you live in a climate where you have freezing weather, turn the pump off in the winter. Most pumps do not function well in freezing water. If you are worried about your pond freezing over, throw an empty plastic gallon jug or several in the water during the freezing weather. In the morning, remove the jug and there will be a hole in the ice so gases can move freely during the day. Be sure to put that jug back in the water when the freezing weather returns at night.