Rather than provide a water-down and very rushed account of Greek culture and civilization, I would rather give you a short list of very useful web-links, which you can download and print off as required. There is a veritable Olympian amount of information out there, in fact a quick search on any search engine will produce more information than you could use!
Daily Life In Ancient Greece
I recommend this site. It's aimed at students, but is broad in scope, easy to read and includes all the pertinent information you need to get a handle on Greek culture. You'll undoubtedly want to progress to more sophisticated sites, but as a primer it can't be beat.
Perseus
This amazing web tool gives you instant access to almost the entirety of Greek and Roman texts in translation. The Perseus Encyclopedia can give you references and material on any subject you like. Type in 'delphi' and scroll through 333 references in Greek and Roman texts (including some fine descriptions of the location), photos and plans. Sparta, Athens, Philip ... you'll be spoilt for choice.
Argos
This site gives you access to a huge array of ancient sites, nearly all essays and articles written by experts in their subject. You'll be amazed at what you can read about here. From coinage to religious festivals, ship design to the rise of Macedon.
Ancient Greek Sites on the WWW
A nice collection of useful and interesting Greek web-sites.
Classical Myth: The Ancient Sources
A fantastic resource; not only including a range of images of each god, but also translated source texts in which they are mentioned. Great!
Delphi
A useful article on this magical Greek site
Ancient Greece
Quite a comprehensive site, covering people, places, history politics and philosophy.It has a very useful list of links too!
Map of Athens
Map of Ancient Greece
Map of Central & Southern Greece
The Greek texts are full of incident, character and authentic situations. Dipping into any of these will reward the GM who wants to stop pretending what it was like, and instead actually go there and speak to someone who lived in the 4th or 5th century BC. Modern translations are lucid, easy to read and filled with modern energy. There are lots of texts available in translation. I offer here only those I found most useful in conjuring up the style of Heroes of Delphi.
Arrian, The Campaigns of Alexander
Arrian, a Roman historian, wrote the best and fullest account of Alexander's life. It is of course an epic story and Arrian's concentration on detail really gives you the feeling that you march alongside the army. The siege of Tyre is a wonder! You have to stop reading now and then to remember "this actually happened, this isn't a story". Find out about life, about Persia, about the Greek military and the mindset of the ancients. And read about my favourite character from ancient history - Alexander, part-man, part-god, part-lunatic.
Homer, The Iliad
OK, we're out by 1,000 years but Homer was the 'Bible of the Greeks', recited at feasts and banquets, quoted by playwrights and politicians. To be Greek one had to know the language and speak some Homer. This is the great account of the Achilles and his tantrum at the Siege of Troy. There are gods fighting hand to hand, chariots, blood and gore, magic, epic battle scenes, death and blood and more gore, discussions on Olympus and more. Forget those cheesy Harryhausen movies - this book is the only Greek epic you need! Easy to read and absolutely wonderfully written with colour and poetry.
"Agamemmnon said no more, and his driver whipped his long-maned horses and started them towards the hollow-ships. The pair flew off with a will, and their breasts were flecked with foam, their bellies grey with dust, as they carried off the wounded King from the battlefield."
Herodotus, The Histories
Contemporary with Thucydides, Herodotus instead looked back. Back to the Persian Wars and to the Persian Empire. Less a historical account, The Histories read like the long fire-side tales of a veteran Greek traveller full of fairy tales and strange customs, barbarians and cults from faraway places. Actually The Histories are jam-packed full of accurate detail on Egypt, Scythia, Persia and elsewhere. Although you can find better accounts of these cultures in modern books, The Histories give you wonderful tales, places and events. It shows the ancient world (outside of Greece) to be a wonderful, colourful and vibrant place full of people. An easy read but long.
Plutarch, The Age of Alexander
A very easy book, this. Plutarch was a Roman historian who specialised in short biographies. Here are a number of Greek personalities from the 4th century. Because the book looks at different people in different places The Age of Alexander is easy to read, and you don't get bored. The focus of Plutarch's work are great warriors and statesmen, there's plenty of action either on or off the battlefield. Alexander is included here, but my favourite is Pyrrhus, a mercenary general par excellence who fought for Magna Graecia. The story of his death, during bitter street fighting inside the walls of Argos is amazing. A general who was supposed to have cleaved an enemy in half with one stroke - killed by a roof-tile thrown by an Argive woman! Fantastic stuff!
Thucydides, History of the Peloponnesian War
This book is the definitive account of Greece at war. It was written by an Athenian who experienced it from both sides and is a clean, crisp and concise account of the politics, strategy and the battlefield tactics. Nothing is missed and the down-to-earth situations are never forgotten. It is a very human account, but like the war itself is long, complex and on occasion difficult to follow. But still, it is my most treasured translation. Greece at war: how, why, where - here.
Xenophon, The Persian Expedition
The account of a Greek mercenary general who took an army of 10,000 hoplites to fight in a Persian civil war. When his side lost, Xenophon had to fight and march and fight his way back to Greece. A harrowing, epic, brutal and breathtaking true story. An easy read and a rewarding one.