Building materials: Initial wood then transition to stone. The stone would be mostly marble but could be sandstone with a marble stucco. Doors would be made of elm or cypress with bronze medallions.
Roof Structure: Ancient Greek architecture uses the post and lintel system.
The simplest design of any order. Seen in the column and temple design. Doric columns would rest directly on the building floor, it has no base. The columns are wider on the bottom and taper towards the top. Each column has 20 flutes.
attribution: Napoleon Vier from nl [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], from Wikimedia Commons
More ornate then ionic. Taller and slimmer then ionic. Each column has 24 flutes.
Most ornate of the three. Mostly used by the Romans. Not as common in Greek architecture. Capitals emulate flowers and leaves. The frieze to architrave ratio is 1:1. Each column has 24 flutes.
Public Square Area (Agora)
The public square area of an Ancient Greek town would consists of the main Temple, minor temples, stoa, bauleuterion, and farmer's market.
There would be a main temple in the center of town at the highest point. The typical column count of at temple is n=2d+1 (n = # of columns on long side, d= # of columns on short side). Length is between 30-60m. Temples would have 3 steps leading into the temple. There are several styles of temple but they all share one common feature of a single room with no windows that housed the statue of a god.
Attribution: By Athinaios adapted to English (Benutzer:Fjellfross, Image:Antike-tempel-arten.gif) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons
A stoa is an area of shops at the edge of the agora. The shops sold more high end objects. It is a 2 story structure with 21 shop stalls on the second floor.
The bouleterion is the center of government for an ancient Greek town. Also housed the city council.
Houses had no one particular design and were either 1 or 2 stories. The second story would be dedicated space for the women of the house. The houses were stone with plastered exterior with fresco inner walls. House of the wealthy would have mosaic floors.
The theater was constructed on the slop of the hill to take advantage of the slop to construct the terraced seating. It is common to have a temple close by the theater because of the strong connection of drama and religion.
Attribution: By Leftezi English captions: Flyax (File:Ancient_greek_theater_greek.svg) [CC-BY-3.0 (http://creativecommons.org/licenses/by/3.0)], via Wikimedia Commons
The gymnasium was the center for exercise, bathing, and education for men in ancient Greece. There was individual spaces for a variety of activities and lectures. Sometime but not always a stadium would be connected to the gymnasium. The stadium was 180 m long and was used for foot races.
(Not easy to find a good diagram. This is the best I've found.)
http://www.ancientgreece.co.uk/acropolis/challenge/cha_set.html (build your own temple)