Pad Thai is basically a rice noodle dish, quick fried with fish sauce. Flavoring comes from the fish sauce of course, small tamarind pieces or pulp, the wonderful sticky sweetness of palm sugar, and if you're willing - a small amount of some wonderful Thailand hot chiles!
The most common of the secondary flavoring ingredients include garlic, dried shrimps, shallots, scallions, garlic chives, pickled turnips (definitely optional) and more - but these seem to be the Pad Thai ingredients that you're most likely to encounter.
The best Pad Thai can usually be found served up in fried egg, although it seems to be common in the West to leave out this key ingredient. While Pad Thai in Thailand tends to be light and dry, and features the egg prominently, Pad Thai in western countries tends to be heavier, and sport less ingredients and have a thick reddish oily consistency. It's unclear why this should be the case, but sampling a reasonable amount of Pad Thai in Thailand and elsewhere can only lead to that observation!
(And in case you didn't believe us about every Thai cook having their own unique recipe for Pad Thai, watch this guy.)
Pad Thai is almost always served with shrimp, and sometimes cooked with chicken, bean sprouts or tofu. A light drizzling of lime juice is typically added before serving in the Thai version, and it is very common to serve Pad Thai with lime wedges. Finally, crushed roasted peanuts, a common garnish, are often sprinkled over the top. This is a distinguishing feature not typically found in the border areas of neighboring countries like Cambodia and Laos.