I always say that the key to a good, clean, healthy pool water is two things; 1) good water chemistry and 2) good filtration.
So the basics of good filtration. This would start with a clean pool filter that is adequately sized for your swimming pool. Next the pump, regardless of the flow rate, needs to run long enough to turn the full volume of the pool at least once per day.
Now the basics of good water chemistry. You must have enough sanitizer in the water to kill germs, bacteria and algae. If you are using chlorine, then you have maintain a residual of 1.0 to 3.0 parts per million. Next, your sanitizer needs to be properly stabilized. Then your pH needs to be in balance so that your sanitizer is effective.
That's it. Now keep your pool clean. Wait, you still are getting algae? Time to do some higher level testing. I suggest testing for phosphates. Phosphates are the organic stuff that get into your pool from dirt, wind and leaves. Phosphates provide a great source of food for algae, so if you have phosphates in your pool, you are letting algae thrive and grow and drive you crazy.
If you want to keep your sanity, I suggest hiring a reputable pool professional to help you get things under control.
What do I need to know when buying a house with a pool?