Use the placard on your car door as a starting point
A lot of people consider the tire pressure numbers on their car door to be gospel. Others don't even even realize there is a placard on the door. Really, those numbers tell you the absolute minimum pressure required, based on a combination of how much weight they'll have to carry (more weight requires more pressure), and how much pressure is needed to ensure all of the tread hits the ground.
Add more air than the recommended minimum
Measure your tires before you drive, when the tires are at their coldest and thus the pressure is at the lowest. Ideally, you should exceed the recommended minimum by several PSI, then drive the car, paying attention to how it feels. Reduce the pressure ever so slightly, and drive it again, repeating until you find your car's sweet spot. Your car will feel more comfortable -- it will better absorb bumps without harshness, and won’t feel overly stiff, either. Even two to three PSI can make a huge difference in both ride comfort and handling, so if you don't believe me, I urge you to try it.
Bonus: use different pressures for front and rear to change your car's handling
If you're on the enthusiast side of things, and you don't already adjust your front and rear tires to different settings, you're missing out. By increasing or decreasing front pressures, you will greatly reduce understeer or oversteer respectively, and the inverse is true for the rear tires. If you don't know what any of that means, stick with what's the most comfortable and enjoy.
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