There are many variables - but generally, you want to completely circulate the water at least every 2 hours at a absolute minimum. We recommend trying to turn over the water at least every hour. That means that a 1000 gallon pond should have at the absolute minimum a 500 gph pump. But most installations would require a pump= to 1000 gph. Ideal conditions would be a turnover rate of once every 30 minutes. Some systems out today DO NOT require the use of large pumps to properly filter the water. Always use the recommended in-flow rating of the filter. If you want a larger pump, no problem, just use a flow control valve.
It is best to keep the pump circulating water 24 hours a day through out the summer months. Aquatic plants will be adding oxygen to the water during the day time when they are photosynthesising, but during the night this process will stop and the plants will continue to absorb some oxygen for their own use. This leads to a drop in the levels of dissolved oxygen at night. Warmer water also holds less oxygen and the combination of turning off the pump, warm water and a planted pond causes large numbers of fish mortalities every year. There is little risk of this happening during the winter when the colder water will have a much greater oxygen content, but if you have a biological filter system then this still requires a water flow over winter.