Run your pump just enough to keep your water looking great!
In most situations that is going to be a function of water turnover. Most people find that one turnover a day works well. How many hours that will be depends greatly on your pool size relative to your GPM. Typical numbers run in the 8-10 hour range, but can vary dramatically from there. A properly sized small pump pushing water around very slowly 24 hours a day has some advantages, but sometimes you really want a lot of water flow (spa, water features, clearing out algae, some cleaning robots). This is part of why two speed pumps are recommended.
The short answer is, as long as it takes. Most people say you need 1-2 water turnovers per day but you can also just use trial and error to see what your pool needs. Start with about 8 hours per day. If your water stays clean and clear for a few days, reduce the run time by 30 minutes and try it again for a few days. Repeat until your water isn't staying as clear as you'd like.
I say start with 8 because that is usually adequate for most systems. If you have an undersized filter (which is not uncommon) you might actually have to go up from there. I doubt very much you'll be able to run much less than 6 hours a day.
Regular manual or automatic vacuuming and brushing will probably also allow you to reduce pump time somewhat.
Make sure you keep an adequate level of chlorine in the pool regardless of how long you run your system. That's the most important thing from a safety standpoint.
I would advise if you are seriously trying to find out how long you need to run your pump you install a flow meter to verify your flow rates. The trial an error approach also works but you wont really know your turnover rates.
A flow meter is the most accurate method to determine flow rates but if you are only interested in an approximation, just look at the pump's head curve and pick a value that is close to the center. It will usually get you close enough.
I am not sure what your equipment is but from a typical pump head curve for AG pools, your flow rate for a 1 1/2 HP pump is about 40-60 GPM or a turnover of about 3-4 hours. So 8 hours should be more than enough.
Accuracy of turnover rates is not all that important since other factors for pump run time can come into play. How much organic material is dropped in the pool each day, how often is the pool used and does your dog like to swim too are all important factors in determining run time.