this site will give you good insight as to how the various logic gates work.
http://www.play-hookey.com/digital/electronics/of course, it's rarely practical to build logic gates from discrete components anymore. During the cold war, the 4000 and 7400 series of logic chips were popular, now it's all micro controllers and programmable logic devices. Luckily thanks to massive overproduction, the 4000 series is still around and cheap, and they're still building 7400 series chips, many with crazy family names that it would take a lot of study to figure out. 74HC seems to be one of the most common.