If you have hard water, the key to minimising water spots (aside from using a water filter as I do) is to get the car dried off as soon as posibble, especially if it is in direct sunlight which will dry water spots on very quickly. To aid faster drying, leaving the minimum amount of water on the car at the rinse stage, make sure the final rinse is done with an open ended hose. rinsing from roof down. This is an important step and will makes the water sheet of the car and that means less standing water on the car to dry off as opposed to a spray rinse which leaves lots of droplets all over the car, each one a potential water spot.
Before I got a water filter, in summer I used to rinse a few panels at a time then towel dry, starting with those panel in the sun. Takes longer but does reduce the risk of water marks.
To get rid of the ones on your car, first give it another wash, open ended rinse and towel dry as quickly (but carefully) as you can. Also look at a product such as CarPro Spotless which can be applied to reduce/rid water spots. Additionally you might want to think anout using a rinse/dry aid product such as DoDo Juice Time to Dry which speeds up the drying process.
Unfortunately very stubborn water marks may need to be polished out if another wash and the suggestions above don't work.