Do not use whatever pressure you find on the sidewall of the tyre. This is the maximum pressure the tyre is rated for before it starts to become unstable and liable to a blowout. You'll have massively reduced traction, and increased tyre wear.
As others have said, your recommended pressure can be found either in the driver's door jamb (near the catch where the door lock clicks on to), or inside the fuel filler cap (German cars like to do this).
On the sidewall of your tyres will be the tyre's size. It is recorded as (for example) 205/55R16. The first number is the effective width of the tyre in mm, the second number is the tyre sidewall as a percentage of the width (55% of 205mm) and the third number is the diameter of the metal wheel in inches.
All you need to do is match that number to the number on the sticker or in the manual. If it's only ever you or maybe one passenger in the car use the lower of the two indicated pressures. If you often drive fully loaded with passengers or with heavy items in the boot use the higher of the indicated pressures. Make sure you use the right pressures for front and rear as they're often different.
Pressure is often given in PSI, but it may be given in bar or kPa as well. 1 PSI = 6.9kPA = 0.07 bar. Remove your dust caps as soon as you park up in the air pressure bay. When you walk up to the machine set your pressure first - they're often in PSI as standard but if you press and hold the unit button it should change to bar. Set the pressure you require. Insert your money (usually 50p) and then once the compressor starts up, hold the wand to each valve stem until the machine beeps at you. It will automatically release air if the pressure is too high so don't worry about that. Once you're done don't forget to put all your dust caps back on. You can easily do all four tyres in the time it gives you - you should probably check the pressure on your spare tyre as well. It's usually higher so check the manual for that pressure too.
Once you've done it a couple of times it's very easy.