They are the three principal classical orders: Doric, Ionic and Corinthian. Be able to identify these three styles is easy, looking at the architecture of ancient Greece, or of Greek-inspired buildings. However, the thing gets complicated when they move to Rome, where we can also find Tuscan and Composite orders that were inspired by the Doric and the Corinthian respectively. This Merriam-Webster Inc. diagram clearly shows the different styles of capitals and columns for each order.
File:Frontons. A pediment is an element in classical, neoclassical and baroque architecture, and derivatives therefrom, consisting of a gable, originally of a triangular shape, placed above the horizontal structure of the entablature, typically supported by columns. The tympanum, or triangular area within the pediment, was often decorated with relief sculpture depicting scenes from Greek and Roman mythology or allegorical figures.