Leave the M4 at junction 33 and take the A4232 towards Barry and the airport - it's the third exit if you're travelling eastbound, and the first exit if you're travelling westbound.
At the roundabout, take the third exit onto the A4050. Take the second exit at the next six roundabouts, staying on the A4050. Then at the next roundabout, take the second exit onto the A4226.
Take the second exit at the following roundabout, then the first exit at the roundabout after that, into the airport complex, and follow the signs for Long Stay Car Park 2.
If you're using a sat nav, the postcode is CF62 3BD.