Current automotive paint is pretty soft and scratches easily. The waterborne paints just are not as hard as prior paint. In order to remove the small scratches, you have to remove the top layer of the paint down to the level of the bottom of the scratch. To do this you can use one of the many abrasive polishes. Depending on how deep they are, you can use a very fine polish or one that is more aggressive.
Of course, the best way is to avoid the scratches in the first place. Most scratching occurs when you wash and dry the car. Dust and dirt contain very abrasive particles including silica (which is used in some sandpaper). The idea when washing a car is to ensure that the dirt and dust on the paint is not pressed into the paint. This is done by using a constant stream of water on the area being washed and by using a boar's hair brush. Do not dry the car unless it is absolutely clean. The towel will press any left over dirt into the paint. Never even dream of using a chamois to dry a car. The flat surface will combine with even small particles to make a nice piece of sandpaper. Use microfiber towels. If a towel has any discoloration or dirt on it after you use it, you have been scratching the paint.
And - don't let anyone touch your car. Their fingers will simply be pressing any dust into the paint.