Greece's problem is they didn't change their fiscal and monetary policies after joining the EU common currency. The Greek government kept its economic policy which consisted in spending more than it received from taxes and minor state entrepreneurial activities, and, in the past, printing drachmas to make up for its budget deficits. It amounts to a fiscal and monetary policy where tax revenues are produced with the printing press (producing bank notes or bonds). Some countries prefer this system to price stability, which has other advantages and drawbacks.
The Greek government began to borrow euros mostly from foreign investors. Big European lenders (Société Générale, Deutsche Bank, etc.) were happy to lend to Greece, because the interest rate was high, to take into account the risk, and at the same time they knew that Europe would refund them should Greece fail. These were euros flowing into the country and corresponding promises to pay back later including some interests (bonds) flowing out. Private Greek agents too borrowed within the country as well as abroad. In parallel to its budget deficits, Greece trade went into deep imbalance. The country indulged in a spending spree with its new money buying goods and services all over the world much more easily than with its previous drachma. Greece paid its imports in part with exports, in part with promises, and in part with euros, which left the country.
The eurozone, feeling concerned, hesitates on what to do. Meanwhile, the Greek government began to reduce the salaries of civil servants, pensions of retirees and public spending. A growing number of Greeks don't have enough money for their everyday expenditures, and therefore shops and local producers suffer as well. The whole country is simply running out of the official money and its GDP has been decreasing for the last three years.
Go ahead. Tell me I don't have a clue, but please offer up some more insight of your own.