You need constant constant movement to maintain a high level of dissolved oxygen, so a water fall or fountain is the easiest way.
I have a solar pump in my tiniest pond, and it does help a little bit in the sunny part of the day, but is off about 75% of the time, its effect is at best marginal.
Getting rid of the stuff that creates biological oxygen demand also goes along way.
BOD is created by any form of metabolism/breakdown of dissolved organic carbon.
I use a DIY foam fractionator to do that, but it also requires a constantly running pump to accomplish its end result. It removes the stuff that creates Biological Oxygen demand before is gets a chance to metabolize, but also provides media for beneficial bacteria to do its job. The pond below is small, only 500 gallons, and could not support the large bioload for its size it has, in a healthy way, without fractionation or some other manner of filtration. It contains 4 goldfish and 1 medium koi (and their fry).
click on the pic to start the video
