How does dust and dirt harm computers?

Mostly it builds up on the fans and prevents the system from cooling and will lead to shut downs or unpredictable behavior. Using "dust off" or any other compressed air can you can blow the dust out of all of the fans including any fans on the video card if there is one. There are several fans in a normal computer including,

CPU fan mounted on the actual CPU

case fans mounted on the case (could be severel here too)

video card fans are mounted on the video card itself and can be hard to reach(not all video cards have fans mostly just the top end cards)

Also dust can acumulate on your CD roms optics and will prevent the reading of CD's, any standard CD ROM drive cleaner will work to clean it or you can use a que tip with rubbing alcohol to clean it directly.