Should tires be inflated to the vehicle's specifications or the PSI found on the tire itself?
Tires should be inflated to the vehicle manufacturer's recommendation for your vehicle. Do not use the pressure indicated on the sidewall of the tire as this is the maximum inflation pressure for the tire itself, not for the tire when used on your specific vehicle.
Your vehicles recommended tire pressure can be found on the vehicle tire information door placard - typically located on the inside door panel or the door itself. It may also be in the owners manual or on a decal in your glove box.
NOTE: Pressure level may be different for the front and rear tires.
Recommended tire pressures are given for cold (not recently driven) tires. Check tire pressure in the morning or after the vehicle has been sitting for a couple of hours. Driving heats up the tires, causing the air inside to expand, giving an artificially high reading.
Use a good quality, accurate tire gauge. The built in gauge on an air hose or compressor is typically inaccurate.